Question 1

Name the rule of inference ( p . q ) ? ( q . p )&#10;A)Distribution&#10;B)Commutation&#10;C)Association&#10;D)Exportation

Accepted Answer

The rule of inference that allows the interchange of the positions in a conjunction (from $ p \cdot q $ to $ q \cdot p $) is called Commutation.

Question 2

If (?x ) ~ Mx is true , then (x) Mx is _____________&#10;A)valid&#10;B)true&#10;C)false&#10;D)true or false

Accepted Answer

The statement "(∀x) ~Mx" means "for all x, not Mx is true," which implies that there is no x for which Mx is true. Therefore, the statement "(∃x) Mx" (there exists an x for which Mx is true) is false. Since "(∀x) Mx" (for all x, Mx is true) is a stronger claim than "(∃x) Mx," it must also be false if "(∃x) Mx" is false.

Question 3

If (x) ( H x ? Mx ) is true, then (?x ) ( H x . ~Mx ) is ___________&#10;A)false&#10;B)true or false&#10;C)true&#10;D)valid

Accepted Answer

The first statement says that for all x, if x is H then x is M. The second statement claims there exists an x such that x is H and not M, which contradicts the first statement. Therefore, if the first statement is true, the second must be false.

Question 4

Bi-conditional statement is also called _____________&#10;A)implication&#10;B)material equivalence&#10;C)material implication&#10;D)logical equivalence

Accepted Answer

A bi-conditional statement is also known as material equivalence, as it asserts that both statements are equivalent, meaning both are true or both are false.

Question 5

The negation of p v q is symbolised as&#10;A)~p v q&#10;B)p v ~q&#10;C)~(p v q)&#10;D)~ p v ~q

Accepted Answer

The negation of a disjunction (p v q) is symbolized as the negation of the entire expression, which is written as ~(p v q). This applies De Morgan's laws, which state that the negation of a disjunction is the conjunction of the negations.

Question 6

Raju and Manu will both not win is symbolised as&#10;A)~ R v M&#10;B)~(R.M)&#10;C)R v ~M&#10;D)~R.~M

Accepted Answer

The correct symbolisation for "Raju and Manu will both not win" is "~R.~M." This means "not Raju and not Manu," indicating that neither Raju nor Manu will win.

Question 7

By using symbols, we can ___________the validity of an argument quickly and accurately&#10;A)combine&#10;B)determine&#10;C)deny&#10;D)negation

Accepted Answer

Using symbols allows for the precise and efficient assessment of an argument's validity, as it enables the application of formal logic principles.

Question 8

A statement can be replaced only by a statement logically __________to it .&#10;A)different&#10;B)vague&#10;C)equivalent&#10;D)contradiction

Accepted Answer

A statement can be logically replaced by another statement only if the two statements are equivalent, meaning they have the same truth value in every possible scenario.

Question 9

By _______________, the left-hand conjunct can be switched over to the right-hand&#10;A)association&#10;B)distribution&#10;C)exportation&#10;D)commutation

Accepted Answer

Commutation is the logical principle that allows for the switching of the positions of conjuncts in a conjunction. It states that if a conjunction $P \land Q$ is true, then $Q \land P$ is also true, reflecting the commutative property of logical conjunction.

Question 10

The negation of the conjunction of two statements is logically equivalent to __________ of their negation.&#10;A)disjunction&#10;B)conjunction&#10;C)implication&#10;D)negation

Accepted Answer

The negation of the conjunction of two statements (not (P and Q)) is logically equivalent to the disjunction of their negations (not P or not Q), according to De Morgan's laws.

Question 11

Name the rule of replacement (P ? q)? [(p.q) v (~p.~q)]&#10;A)Exportation&#10;B)Material Equivalence&#10;C)Transposition&#10;D)Association

Accepted Answer

The answer of Name the rule of replacement (P ?...

Question 12

If (?x ) Mx is true, then (?x ) ~Mx is ____________&#10;A)true&#10;B)true or false&#10;C)valid&#10;D)false

Accepted Answer

The answer of If (?x ) Mx is true, then...

Question 13

Conjunction, Disjunction,Implication and biconditional are called Truth ________ connectives&#10;A)contradictory&#10;B)contrary&#10;C)hidden&#10;D)functional

Accepted Answer

The answer of Conjunction, Disjunction,Implication and biconditional are called Truth...

Question 14

A general proposition is formed from a propositional function by placing either a universal or an existential __________before it.&#10;A)variable&#10;B)quantifier&#10;C)reference&#10;D)denotation

Accepted Answer

The answer of A general proposition is formed from a...

Deck 16: Logic and Propositional Functions