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If the Boolean expression \((p \Rightarrow q)\Leftrightarrow (q\, *(\sim p))\) is a tautology, then the Boolean expression \(p\, *(\sim q)\) is equivalent to :

(1) \(q \Rightarrow p\)

(2) \(\sim q \Rightarrow p\)

(3) \(p \Rightarrow \sim q\)

(4) \(p \Rightarrow q\)

in MATHEMATICAL REASONING by Expert (11.5k points) | 119 views

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Best answer

Answer: (a)

(p → q) ⇔ (q * ~ P)

p

q

p → q

q * ~ P

~ q

~ q ∧ p

~ (~ q ∧ p)

T

T

T

T

F

F

T

T

F

F

F

T

T

F

F

T

T

T

F

F

T

F

F

T

T

T

F

T

∴ ~ (~ q ∧ p) = q ∨ ~ p = ~ p ∨ q

∴ * is equivalent to ∨

∴ p * ~ q = p ∨~ q

= ~ q ∨ p

= q⇒ p

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