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What is a truth table and how is it constructed?

• A truth table is a method for solving equations in calculus.

• A truth table is a table that shows all possible truth values for a logical expression based on its variables.

• A truth table is a list of all possible outcomes of a game.

• A truth table is a diagram that represents the flow of a program.

Using logical symbols, express the statement: 'If it rains, then the ground is wet.'

• ¬p → ¬q

• p ∧ q

• p → q

• q → p

Prove the logical equivalence of (P ∧ Q) and (Q ∧ P).

• False

• True

• Only if Q is true

• Only if P is true

How do you solve the logical problem: 'If A is true and B is false, what is the value of A ∨ B?'

• true

• false

• null

• undefined

Create a truth table for the expression: (P ∨ Q) → R.

• (P ∧ Q) → R

• (P ∨ Q) ∧ R

• P → (Q ∨ R)

• [[P, Q, R, (P ∨ Q), (P ∨ Q) → R], [T, T, T, T, T], [T, T, F, T, F], [T, F, T, T, T], [T, F, F, T, F], [F, T, T, T, T], [F, T, F, T, F], [F, F, T, F, T], [F, F, F, F, T]]

What does the symbol '¬' represent in logic?

• Conjunction

• Disjunction

• Negation

• Implication

Demonstrate the proof of De Morgan's Laws using truth tables.

• ¬(A ∧ B) = A ∨ B

• De Morgan's Laws: 1) ¬(A ∧ B) = ¬A ∨ ¬B; 2) ¬(A ∨ B) = ¬A ∧ ¬B

• ¬(A ∧ B) = ¬A ∧ B

• ¬(A ∨ B) = A ∨ ¬B

If P is true and Q is false, what is the result of P → (Q ∧ R)?

• true

• undefined

• true or false

• false

Explain the difference between a tautology and a contradiction in logic.

• A tautology can be false; a contradiction can be true.

• A tautology is sometimes true; a contradiction is sometimes true.

• A tautology is always false; a contradiction is always true.

• A tautology is always true; a contradiction is always false.

Solve the logical expression: (P ∧ ¬Q) ∨ (¬P ∧ Q).

• False if P is true and Q is false

• True if P is false and Q is false

• True if both P and Q are true

• True if P and Q are different, False if they are the same.