Deck 11: Predicate Logic

Question 1

Identify the quantity and quality of the following statement form. Every S is P.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Answer 1

A

Question 2

Identify the quantity and quality of the following statement form. Not a single S is P.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Answer 2

B

Question 3

Identify the quantity and quality of the following statement form. There is an S that is not P.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Answer 3

D

Question 4

(y)By is called a(n) _____ sentence and the variable y is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 5

( $\exists$ z)Nz is called a(n) _____ sentence and the variable z is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 6

~(x)Nz is called a(n) _____ sentence and the variable z is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 7

Nz is called a(n) _____ sentence and the variable z is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 8

Identify the quantity and quality of the following statement form. Some shopping carts have squeaky wheels.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 9

Identify the type of statement represented by the following. MA

A)open sentence
B)singular
C)quantified existential
D)quantified universal
E)None of these answers are correct.

Question 10

Identify the type of statement represented by the following. ( $\exists$ x)Fx

A)open sentence
B)singular
C)quantified existential
D)quantified universal
E)None of these answers are correct.

Question 11

Pa is called a(n) _____ sentence and the constant "a" is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 12

Identify the type of statement represented by the following. (x)Ex

A)open sentence
B)singular
C)quantified existential
D)quantified universal
E)None of these answers are correct.

Question 13

Identify the type of statement represented by the following. Pa

A)open sentence
B)singular
C)quantified existential
D)quantified universal
E)None of these answers are correct.

Question 14

Px is called a(n) _____ sentence and the variable x is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 15

( $\exists$ x)Px is called a(n) _____ sentence and the variable x is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 16

Identify the quantity and quality of the following statement form. Any S is P.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 17

Symbolize the following statement form. Some A are not B.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 18

Identify the type of statement represented by the following. Px

A)open sentence
B)singular
C)quantified existential
D)quantified universal
E)None of these answers are correct.

Question 19

Identify the quantity and quality of the following statement form. There is an S that is a P.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 20

(x)Nz $\supset$ Pa is called a(n) _____ sentence and the variable z is said to be _____.

A)open; free
B)closed; bound
C)open; bound
D)closed; free
E)None of these answers are correct.

Question 21

Symbolize the following statement. Some of Kepler's conclusions were mistaken.

A)(x)(Kx $\supset$ Mx)
B)(x)(Kx $\supset$ ~Mx)
C)( $\exists$ x)(Kx • Mx)
D)( $\exists$ x)(Kx • ~Mx)
E)None of these answers are correct.

Question 22

Identify the quantity and quality of the following statement form. All babies cry.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 23

Symbolize the following statement. Some mathematicians are good teachers.

A)(x)(Mx $\supset$ Gx)
B)(x)(Mx $\supset$ ~Gx)
C)( $\exists$ x)(Mx • Gx)
D)( $\exists$ x)(Mx • ~Gx)
E)None of these answers are correct.

Question 24

Symbolize the following statement. Some baseball players do not take performance-enhancing drugs.

A)(x)(Bx $\supset$ Tx)
B)(x)(Bx $\supset$ ~Tx)
C)( $\exists$ x)(Bx • Tx)
D)( $\exists$ x)(Bx • ~Tx)
E)None of these answers are correct.

Question 25

Identify the quantity and quality of the following statement. (x)(Fx $\bigvee$ Gx)

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 26

Identify the quantity and quality of the following statement. (x)(Fx $\supset$ ~Gx)

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 27

Symbolize the following statement. All rocks break windows.

A)(x)(Rx $\supset$ Bx)
B)(x)(Rx $\supset$ ~Bx)
C)( $\exists$ x)(Rx • Bx)
D)( $\exists$ x)(Rx • ~Bx)
E)None of these answers are correct.

Question 28

Symbolize the following statement form. Some A are B.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 29

Symbolize the following statement. No astronomers believe in astrology.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 30

Symbolize the following statement. Many types of mushrooms are not poisonous to humans.

A)(x)(Mx $\supset$ Px)
B)(x)(Mx $\supset$ ~Px)
C)( $\exists$ x)(Mx • Px)
D)( $\exists$ x)(Mx • ~Px)
E)None of these answers are correct.

Question 31

Symbolize the following statement. Some monks were geneticists.

A)(x)(Mx $\supset$ Gx)
B)(x)(Mx $\supset$ ~Gx)
C)( $\exists$ x)(Mx • Gx)
D)( $\exists$ x)(Mx • ~Gx)
E)None of these answers are correct.

Question 32

Symbolize the following statement form. All A are B.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 33

Identify the quantity and quality of the following statement form. Some colleges do not have entrance requirements.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 34

Symbolize the following statement. All pentagons have five sides.

A)(x)(Px $\supset$ Fx)
B)(x)(Px $\supset$ ~Fx)
C)( $\exists$ x)(Px • Fx)
D)( $\exists$ x)(Px • ~Fx)
E)None of these answers are correct.

Question 35

Identify the quantity and quality of the following statement. (x)(Fx $\supset$ Gx)

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 36

Identify the quantity and quality of the following statement. ( $\exists$ x)(Fx • Gx)

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 37

Symbolize the following statement form. No A are B.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 38

Identify the quantity and quality of the following statement. ( $\exists$ x)(Sx • ~Px)

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 39

Identify the quantity and quality of the following statement form. Some football players are business majors.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 40

Identify the quantity and quality of the following statement form. Everyone likes to discuss the weather.

A)quantity: universal; quality: affirmative
B)quantity: universal; quality: negative
C)quantity: particular; quality: affirmative
D)quantity: particular; quality: negative
E)None of these answers are correct.

Question 41

Symbolize the following statement. Every psychiatrist is a medical doctor.

A)(x)(Px $\supset$ Mx)
B)(x)(Px $\supset$ ~Mx)
C)( $\exists$ x)(Px • Mx)
D)( $\exists$ x)(Px • ~Mx)
E)None of these answers are correct.

Question 42

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a crocodile $\quad$$\quad$$\quad$$\quad$$\mathrm { M } x = x$ makes a good pet
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { C } x \cdot \sim \mathrm { M } x )$

A)All crocodiles make good pets.
B)No crocodiles make good pets.
C)Some crocodiles make good pets.
D)Some crocodiles do not make good pets.
E)None of these answers are correct.

Question 43

Symbolize the following statement. Every teacher is a saint.

A)(x)(Tx $\supset$ Sx)
B)(x)(Tx $\supset$ ~Sx)
C)( $\exists$ x)(Tx • Sx)
D)( $\exists$ x)(Tx • ~Sx)
E)None of these answers are correct.

Question 44

Symbolize the following statement form. Many A are B.

A)(x)(Ax $\supset$ Bx)
B)(x)(Ax $\supset$ ~Bx)
C)( $\exists$ x)(Ax • Bx)
D)( $\exists$ x)(Ax • ~Bx)
E)None of these answers are correct.

Question 45

Symbolize the following statement. Many types of cactus plants have lost true leaves.

A)(x)(Cx $\supset$ Lx)
B)(x)(Cx $\supset$ ~Lx)
C)( $\exists$ x)(Cx • Lx)
D)( $\exists$ x)(Cx • ~Lx)
E)None of these answers are correct.

Question 46

Symbolize the following statement. Most insects hatch from eggs.

A)(x)(Ix $\supset$ Hx)
B)(x)(Ix $\supset$ ~Hx)
C)( $\exists$ x)(Ix • Hx)
D)( $\exists$ x)(Ix • ~Hx)
E)None of these answers are correct.

Question 47

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a chemical element $\quad$$\quad$$\quad$$\quad$$\quad$$\mathrm { M } x = x$ is a metal
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { C } x \cdot \mathrm { M } x )$

A)All chemical elements are metals.
B)No chemical elements are metals.
C)Some chemical elements are metals.
D)Some chemical elements are not metals.
E)None of these answers are correct.

Question 48

Symbolize the following statement. Many of the transcendentalists came from New England.

A)(x)(Tx $\supset$ Nx)
B)(x)(Tx $\supset$ ~Nx)
C)( $\exists$ x)(Tx • Nx)
D)( $\exists$ x)(Tx • ~Nx)
E)None of these answers are correct.

Question 49

Symbolize the following statement. Some inventors do not file patent applications.

A)(x)(Ix $\supset$ Fx)
B)(x)(Ix $\supset$ ~Fx)
C)( $\exists$ x)(Ix • Fx)
D)( $\exists$ x)(Ix • ~Fx)
E)None of these answers are correct.

Question 50

Symbolize the following statement. Some politicians are corrupt.

A)(x)(Px $\supset$ Cx)
B)(x)(Px $\supset$ ~Cx)
C)( $\exists$ x)(Px • Cx)
D)( $\exists$ x)(Px • ~Cx)
E)None of these answers are correct.

Question 51

Symbolize the following statement. A few English monarchs were not completely sane.

A)(x)(Mx $\supset$ Sx)
B)(x)(Mx $\supset$ ~Sx)
C)( $\exists$ x)(Mx • Sx)
D)( $\exists$ x)(Mx • ~Sx)
E)None of these answers are correct.

Question 52

Symbolize the following statement. Some Egyptians are members of the Muslim Brotherhood.

A)(x)(Ex $\supset$ Mx)
B)(x)(Ex $\supset$ ~Mx)
C)( $\exists$ x)(Ex • Mx)
D)( $\exists$ x)(Ex • ~Mx)
E)None of these answers are correct.

Question 53

Symbolize the following statement. No modern physicists use epicycles to explain the motion of the planets.

A)(x)(Mx $\supset$ Ex)
B)(x)(Mx $\supset$ ~Ex)
C)( $\exists$ x)(Mx • Ex)
D)( $\exists$ x)(Mx • ~Ex)
E)None of these answers are correct.

Question 54

Symbolize the following statement. All objects that have mass have a specifiable quantity of matter.

A)(x)(Hx $\supset$ Sx)
B)(x)(Hx $\supset$ ~Sx)
C)( $\exists$ x)(Hx • Sx)
D)( $\exists$ x)(Hx • ~Sx)
E)None of these answers are correct.

Question 55

Symbolize the following statement. At least one U.S.president was a Quaker.

A)(x)(Px $\supset$ Qx)
B)(x)(Px $\supset$ ~Qx)
C)( $\exists$ x)(Px • Qx)
D)( $\exists$ x)(Px • ~Qx)
E)None of these answers are correct.

Question 56

Symbolize the following statement. Some rules of logic are hard to remember.

A)(x)(Rx $\supset$ Hx)
B)(x)(Rx $\supset$ ~Hx)
C)( $\exists$ x)(Rx • Hx)
D)( $\exists$ x)(Rx • ~Hx)
E)None of these answers are correct.

Question 57

Symbolize the following statement. Construction crews are noisy.

A)(x)(Cx $\supset$ Nx)
B)(x)(Cx $\supset$ ~Nx)
C)( $\exists$ x)(Cx • Nx)
D) $\exists$ x)(Cx • ~Nx)
E)None of these answers are correct.

Question 58

Symbolize the following statement. All quadratic functions have parabolic graphs.

A)(x)(Qx $\supset$ Px)
B)(x)(Qx $\supset$ ~Px)
C)( $\exists$ x)(Qx • Px)
D)( $\exists$ x)(Qx • ~Px)
E)None of these answers are correct.

Question 59

Symbolize the following statement. Some sporting events do not create great revenues.

A)(x)(Sx $\supset$ Cx)
B)(x)(Sx $\supset$ ~Cx)
C)( $\exists$ x)(Sx • Cx)
D)( $\exists$ x)(Sx • ~Cx)
E)None of these answers are correct.

Question 60

Symbolize the following statement. No triangles have four angles.

A)(x)(Tx $\supset$ Fx)
B)(x)(Tx $\supset$ ~Fx)
C)( $\exists$ x)(Tx • Fx)
D)( $\exists$ x)(Tx • ~Fx)
E)None of these answers are correct.

Question 61

The statement Mb is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 62

The statement Fa is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 63

Translate the following symbolized categorical statement into English using the provided key. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\mathrm{B} x=x \text { is a badger } \quad \mathrm{M} x=x \text { is mortal }$
$(x)(\mathrm{B} x \supset \mathrm{M} x)$

A)All badgers are mortal.
B)No badger is mortal.
C)Some badgers are mortal.
D)Some badgers are not mortal.
E)None of these answers are correct.

Question 64

The statement Aa is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 65

The statement [(Da • Ra) • (Nb $\bigvee$ La)] $\supset$ (Ra • Sa) is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 66

The statement Za $\supset$ ~Wa is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 67

The statement (x)Fx • ~( $\exists$ x)Fx is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 68

The statement Fa $\supset$ Ga is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 69

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { P } x = x$ is a piece of paper $\quad$$\quad$$\quad$$W x = x$ is colored white
$( \exists x ) ( \mathrm { Px } \cdot \mathrm { W } x )$

A)All pieces of paper are colored white.
B)No pieces of paper are colored white.
C)Some pieces of paper are colored white.
D)Some pieces of paper are not colored white.
E)None of these answers are correct.

Question 70

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { C } x = x$ is a comet $\quad$$\quad$$\quad$$\quad$$\mathrm { E } x = x$ travels in an elliptical orbit
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( x ) ( \mathrm { C } x \supset \mathrm { E } x )$

A)All comets travel in elliptical orbits.
B)No comets travel in elliptical orbits.
C)Some comets travel in elliptical orbits.
D)Some comets do not travel in elliptical orbits.
E)None of these answers are correct.

Question 71

The statement Mc is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 72

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { B } x = x$ was an inductee into the Baseball Hall of Fame
$\quad$$\quad$$\quad$ $\mathrm { G } x = x$ was born in Georgia
$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { B } x \cdot \mathrm { G } x )$

A)All inductees into the Baseball Hall of Fame were born in Georgia.
B)No inductees into the Baseball Hall of Fame were born in Georgia.
C)Some inductees into the Baseball Hall of Fame were born in Georgia.
D)Some inductees into the Baseball Hall of Fame were not born in Georgia.
E)None of these answers are correct.

Question 73

Translate the following symbolized categorical statement into English using the provided key. W $x = x$ was a wife of King Henry VIII $\quad \mathrm { B } x = x$ lived beyond 30 years of age
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { W } x \cdot \sim \mathrm { B } x )$

A)All wives of King Henry VIII lived beyond 30 years of age.
B)No wives of King Henry VIII lived beyond 30 years of age.
C)Some wives of King Henry VIII lived beyond 30 years of age.
D)Some wives of King Henry VIII did not live beyond 30 years of age.
E)None of these answers are correct.

Question 74

Translate the following symbolized categorical statement into English using the provided key. $\mathrm { A } x = x$ is an avocado tree $\quad$$\quad$$\mathrm { C } x = x$ grows in California
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$( \exists x ) ( \mathrm { Ax } \cdot \mathrm { C } x )$

A)All avocado trees grow in California.
B)No avocado trees grow in California.
C)Some avocado trees grow in California.
D)Some avocado trees do not grow in California.
E)None of these answers are correct.

Question 75

Translate the following symbolized categorical statement into English using the provided key. $\mathrm{L} x=x$ is limestone $\quad$$\quad$$\quad$$\quad$$\quad$$\mathrm{M} x=x$ is metamorphic
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$(x)(\mathrm{L} x \Rightarrow?\mathrm{M} x)$

A)All limestone is metamorphic.
B)No limestone is metamorphic.
C)Some limestone is metamorphic.
D)Some limestone is not metamorphic.
E)None of these answers are correct.

Question 76

Translate the following symbolized categorical statement into English using the provided key. Lx =x is a human language Mx= x is modality-independent
(x)(Lx $\supset$ Mx)

A)All human languages are modality-independent.
B)No human languages are modality-independent.
C)Some human languages are modality-independent.
D)Some human languages are not modality-independent.
E)None of these answers are correct.

Question 77

The statement ( $\exists$ x)Fx is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 78

The statement Ab $\bigvee$ Cb is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 79

The statement (x)~Fx is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements

Question 80

The statement ~Mc $\equiv$ Bm is which kind of statement?

A)atomic singular statement
B)truth-functional compound of singular atomic statements
C)quantifier applied to atomic open sentence
D)truth-functional compound of open sentences within the scope of a quantifier
E)truth-functional compound of quantified statements