Truth Tables and Logical Connectives

Conjunction (∧) is True only when both p and q are True. Since q is False, the statement "p ∧ q" is False.

Negation (¬) reverses the truth value of a statement. Since "p ∨ q" is False (disjunction is False when both p and q are False), its negation "¬(p ∨ q)" is True.

Implication (→) is False when the antecedent (p) is True and the consequent (q) is False. Since p is True and q is False, one of the implications is False, making the entire statement "(p → q) ∧ (q → p)" False.

Biconditional (≡) is True when both implications (→) are True. Since "p ∨ q" is True (disjunction is True when at least one of p or q is True) and "¬p ∧ ¬q" is False (conjunction is False when both p and q are False), the biconditional statement is True.

Implication (→) is True when the antecedent (p ∧ q) is False or the consequent (¬p) is True. Since "p ∧ q" is False and "¬p" is True, the implication "(p ∧ q) → ¬p" is True.

Negation (¬) reverses the truth value of a statement. Since "p ∨ q" is True (disjunction is True when at least one of p or q is True), its negation "¬(p ∨ q)" is False.

Biconditional (≡) is True when both implications (→) are True. Since "p → q" is True (implication is True when the antecedent is False) and "¬q → ¬p" is True (implication is True when the antecedent is False), the biconditional statement is True.

Disjunction (∨) is True when at least one of the statements is True. Since "p ∧ q" is False and "¬p ∧ ¬q" is True, the disjunction "(p ∧ q) ∨ (¬p ∧ ¬q)" is True.

Negation (¬) reverses the truth value of a statement. Since "p → q" is False (implication is False when the antecedent is True and the consequent is False), its negation "¬(p → q)" is True.

Implication (→) is True when the antecedent (p ∨ q) is False or the consequent (p ∧ q) is True. Since "p ∨ q" is True and "p ∧ q" is False, the implication "(p ∨ q) → (p ∧ q)" is True.

Biconditional (≡) is True when both implications (→) are True. Since "p ∧ q" is False (conjunction is False when both p and q are False) and "¬p ∨ ¬q" is True (disjunction is True when at least one of ¬p or ¬q is True), the biconditional statement is True.

Disjunction (∨) is True when at least one of the statements is True. Since both "p → q" and "q → p" are True (implication is True when the antecedent implies the consequent), the disjunction "(p → q) ∨ (q → p)" is True.

Negation (¬) reverses the truth value of a statement. Since "p ∧ q" is False (conjunction is False when both p and q are False), its negation "¬(p ∧ q)" is True.

Biconditional (≡) is True when both implications (→) are True. Since "p ∨ q" is True (disjunction is True when at least one of p or q is True) and "¬p → q" is True (implication is True when the antecedent is False), the biconditional statement is True.

Implication (→) is False when the antecedent (p ∧ q) is True and the consequent (p ∨ q) is False. Since "p ∧ q" is False and "p ∨ q" is True, the implication "(p ∧ q) → (p ∨ q)" is False.