Question 1

What is the rule of inference used in the following:
If it snows today, the university will be closed. The university will not be closed today. Therefore, it did not
snow today.

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Question 2

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\neg \forall x ( F ( x ) \rightarrow \neg M ( x ) )$$

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Question 3

Explain why the negation of "Some students in my class use e-mail" is not "Some students in my class do not
use e-mail".

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Question 4

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\forall x ( \neg ( M ( x ) \wedge \neg F ( x ) ) )$$

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Question 5

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B".
Suppose the universe of discourse consists of all sets. Translate the statement into symbols.
-The empty set is a subset of every ﬁnite set.

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Question 6

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\forall x ( \neg M ( x ) \vee \neg F ( x ) )$$

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The answer of Match the statement in symbols with one...

Question 7

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\neg \exists x ( M ( x ) \wedge F ( x ) )$$

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The answer of Match the statement in symbols with one...

Question 8

write the negation of the statement in good English. Don't write "It is not true that . . . ."
-All integers ending in the digit 7 are odd.

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Question 9

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B".
Suppose the universe of discourse consists of all sets. Translate the statement into symbols.
-Every subset of a ﬁnite set is ﬁnite.

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Question 10

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B".
Suppose the universe of discourse consists of all sets. Translate the statement into symbols.
-Not all sets are ﬁnite.

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Question 11

write the negation of the statement in good English. Don't write "It is not true that . . . ."
-No tests are easy.

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Question 12

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B".
Suppose the universe of discourse consists of all sets. Translate the statement into symbols.
-No inﬁnite set is contained in a ﬁnite set.

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Question 13

write the negation of the statement in good English. Don't write "It is not true that . . . ."
-Some bananas are yellow.

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Question 14

write the negation of the statement in good English. Don't write "It is not true that . . . ."
-Roses are red and violets are blue.

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Question 15

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\exists x ( F ( x ) \wedge M ( x ) )$$

Accepted Answer

The answer of Match the statement in symbols with one...

Question 16

What is the rule of inference used in the following:
If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will
understand the material. Therefore, if I work all night on this homework, then I will understand the material.

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The answer of What is the rule of inference used...

Question 17

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\neg \forall x ( \neg F ( x ) \vee \neg M ( x ) )$$

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The answer of Match the statement in symbols with one...

Question 18

write the negation of the statement in good English. Don't write "It is not true that . . . ."
-Some skiers do not speak Swedish.

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Question 19

A student is asked to give the negation of "all bananas are ripe".
(a) The student responds "all bananas are not ripe". Explain why the English in the student's response is
ambiguous.
(b) Another student says that the negation of the statement is "no bananas are ripe". Explain why this is not
correct.
(c) Another student says that the negation of the statement is "some bananas are ripe". Explain why this is
not correct.
(d) Give the correct negation.

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The answer of A student is asked to give the...

Question 20

Match the statement in symbols with one of the English statements in this list:
1. Some freshmen are math majors.
2. Every math major is a freshman.
3. No math major is a freshman.
-$$\neg \exists x ( M ( x ) \wedge \neg F ( x ) )$$

Accepted Answer

The answer of Match the statement in symbols with one...

Quiz 1: The Foundations: Logic and Proofs

What is the rule of inference used in the following: If it snows today, the university will be closed. The university will not be closed today. Therefore, it did not snow today.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \forall x ( F ( x ) \rightarrow \neg M ( x ) )$

Explain why the negation of "Some students in my class use e-mail" is not "Some students in my class do not use e-mail".

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\forall x ( \neg ( M ( x ) \wedge \neg F ( x ) ) )$

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -The empty set is a subset of every ﬁnite set.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\forall x ( \neg M ( x ) \vee \neg F ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \exists x ( M ( x ) \wedge F ( x ) )$

write the negation of the statement in good English. Don't write "It is not true that . . . ." -All integers ending in the digit 7 are odd.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -Every subset of a ﬁnite set is ﬁnite.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -Not all sets are ﬁnite.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -No tests are easy.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -No inﬁnite set is contained in a ﬁnite set.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Some bananas are yellow.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Roses are red and violets are blue.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\exists x ( F ( x ) \wedge M ( x ) )$

What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \forall x ( \neg F ( x ) \vee \neg M ( x ) )$

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Some skiers do not speak Swedish.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \exists x ( M ( x ) \wedge \neg F ( x ) )$

Quiz 1: The Foundations: Logic and Proofs

What is the rule of inference used in the following: If it snows today, the university will be closed. The university will not be closed today. Therefore, it did not snow today.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ¬∀x(F(x)→¬M(x))\neg \forall x ( F ( x ) \rightarrow \neg M ( x ) )¬∀x(F(x)→¬M(x))

Explain why the negation of "Some students in my class use e-mail" is not "Some students in my class do not use e-mail".

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ∀x(¬(M(x)∧¬F(x)))\forall x ( \neg ( M ( x ) \wedge \neg F ( x ) ) )∀x(¬(M(x)∧¬F(x)))

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -The empty set is a subset of every ﬁnite set.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ∀x(¬M(x)∨¬F(x))\forall x ( \neg M ( x ) \vee \neg F ( x ) )∀x(¬M(x)∨¬F(x))

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ¬∃x(M(x)∧F(x))\neg \exists x ( M ( x ) \wedge F ( x ) )¬∃x(M(x)∧F(x))

write the negation of the statement in good English. Don't write "It is not true that . . . ." -All integers ending in the digit 7 are odd.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -Every subset of a ﬁnite set is ﬁnite.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -Not all sets are ﬁnite.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -No tests are easy.

let F(A) be the predicate "A is a ﬁnite set" and S(A, B) be the predicate "A is contained in B". Suppose the universe of discourse consists of all sets. Translate the statement into symbols. -No inﬁnite set is contained in a ﬁnite set.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Some bananas are yellow.

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Roses are red and violets are blue.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ∃x(F(x)∧M(x))\exists x ( F ( x ) \wedge M ( x ) )∃x(F(x)∧M(x))

What is the rule of inference used in the following: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ¬∀x(¬F(x)∨¬M(x))\neg \forall x ( \neg F ( x ) \vee \neg M ( x ) )¬∀x(¬F(x)∨¬M(x))

write the negation of the statement in good English. Don't write "It is not true that . . . ." -Some skiers do not speak Swedish.

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - ¬∃x(M(x)∧¬F(x))\neg \exists x ( M ( x ) \wedge \neg F ( x ) )¬∃x(M(x)∧¬F(x))

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \forall x ( F ( x ) \rightarrow \neg M ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\forall x ( \neg ( M ( x ) \wedge \neg F ( x ) ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\forall x ( \neg M ( x ) \vee \neg F ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \exists x ( M ( x ) \wedge F ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\exists x ( F ( x ) \wedge M ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \forall x ( \neg F ( x ) \vee \neg M ( x ) )$

Match the statement in symbols with one of the English statements in this list: 1. Some freshmen are math majors. 2. Every math major is a freshman. 3. No math major is a freshman. - $\neg \exists x ( M ( x ) \wedge \neg F ( x ) )$