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Write truth tables for the statement forms in 12–15. 12. ∼p ∧ q 13. ∼(p ∧ q) ∨ (p ∨ q) 14. p ∧ (q ∧ r) 15. p ∧ (∼q ∨ r)

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These truth tables represent the logical values of the given statement forms for all possible combinations of truth values for the propositional variables p, q, and r.

Truth Tables for Statement Forms:

12. ∼p ∧ q

P Q ~P ~P ∧ Q

T T F F

T F F F

F T T T

F F T F

13. ∼(p ∧ q) ∨ (p ∨ q)

P Q P ∧ Q ~P ∨ Q ~(P ∧ Q) ~P ∨ Q

T T T T F T

T F F T T T

F T F T T T

F F F F T F

14. p ∧ (q ∧ r)

P Q R Q ∧ R P ∧ (Q ∧ R)

T T T T T

T T F F F

T F T F F

T F F F F

F T T T F

F T F F F

F F T F F

F F F F F

15. p ∧ (∼q ∨ r)

P Q R ~Q ~Q ∨ R P ∧ (~Q ∨ R)

T T T F T T

T T F F F F

T F T T T T

T F F T T T

F T T F T F

F T F F F F

F F T T T F

F F F T T F

User Maxim Lanin
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