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Fundamental Concepts of Propositional Logic Quiz

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#1

Which symbol represents the logical AND operation in propositional logic?

∧
Explanation

Symbol for logical AND operation.

#2

What is the role of parentheses in propositional logic expressions?

To indicate the order of operations
Explanation

Parentheses specify the order of logical operations.

#3

If 'p implies q' is false, what can be said about the truth values of p and q?

p is true, q is false
Explanation

Implication is false only when the antecedent is true and consequent is false.

#4

If 'p AND q' is true, what can be said about the truth values of p and q?

Both p and q are true
Explanation

Conjunction is true only when both propositions are true.

#5

In propositional logic, what is the negation of the statement 'p OR q'?

¬p OR ¬q
Explanation

Negation of the disjunction.

#6

Which logical connective has the same truth table as an exclusive OR (XOR)?

NAND
Explanation

NAND gate has the same truth table as XOR.

#7

Which law of propositional logic is represented by the statement 'p OR (q AND r) is equivalent to (p OR q) AND (p OR r)'?

Distributive Law
Explanation

Distributive Law distributes OR over AND.

#8

In propositional logic, what is the inverse of the statement 'If p, then q'?

If ¬p, then ¬q
Explanation

Inverse negates both antecedent and consequent.

#9

Which law of propositional logic is represented by the statement 'p AND (p OR q) is equivalent to p'?

Identity Law
Explanation

Identity Law states p AND (p OR q) = p.

#10

What is the contrapositive of the statement 'If p, then q'?

If ¬p, then ¬q
Explanation

Contrapositive switches and negates antecedent and consequent.

#11

In propositional logic, what is the satisfiability of a compound statement that contains contradictory propositions?

Never satisfiable
Explanation

Contradictory propositions make compound statement unsatisfiable.

#12

Which logical connective is also known as the Sheffer stroke?

NAND
Explanation

Sheffer stroke is NAND operation.

#13

What is the logical equivalence of 'p AND (q OR r)' in terms of 'p AND q' and 'p AND r'?

(p AND q) AND (p AND r)
Explanation

Distributive property of AND over OR.

#14

What is the truth value of the statement 'p AND ¬p'?

False
Explanation

Contradictory statements result in False.

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