Fundamental Concepts of Propositional Logic Quiz

Challenge yourself with fundamental concepts of propositional logic. Test your understanding with 14 questions covering logical connectives, truth tables, and more.

Practice Learn Test

Which symbol represents the logical AND operation in propositional logic?

∨

→

∧

What is the role of parentheses in propositional logic expressions?

To indicate the order of operations

To represent logical connectives

To denote variables

To create comments

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

p is false, q is true

p is true, q is false

Both p and q are false

Both p and q are true

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

p is false, q is true

p is true, q is false

Both p and q are false

Both p and q are true

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

¬p AND ¬q

¬p OR ¬q

p AND q

p OR q

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

AND

NAND

NOR

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)'?

Associative Law

Distributive Law

Commutative Law

Identity Law

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

If q, then p

If ¬q, then ¬p

If ¬p, then ¬q

If p, then q

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

Associative Law

Distributive Law

Commutative Law

Identity Law

#10

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

If ¬q, then ¬p

If ¬p, then ¬q

If q, then p

If p, then q

#11

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

Always satisfiable

Sometimes satisfiable

Never satisfiable

Depends on the context

#12

Which logical connective is also known as the Sheffer stroke?

AND

NAND

NOR

#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) OR (p AND r)

(p AND q) AND (p AND r)

(p AND q) NOR (p AND r)

(p AND q) NAND (p AND r)

#14

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

True

False

Dependent on the values of p

Indeterminate