Let (i) (P ∨ q) ∨ (p ∨ ~ q), (ii) (P ∧ q) ∧ (p �

Let (i) (P ∨ q) ∨ (p ∨ ~ q), (ii) (P ∧ q) ∧ (p ∨ ~ q), (iii) (P ∨ q) ∧ (p ∨ ~ q), (iv) (P ∨ q) ∨ (p ∧ ~ q), which one is tautology(1) (i)(2) (ii)(3) (iii)(4) (iv)

Answer»

Correct option (1) (i)

Explanation:

(i) (P ∨ q) ∨ (p ∨ ~ q) = p ∨ (q ∨ ~ q) = P ∨ t = t

(ii) (P ∨ q) ∧ (p ~ q)

(iii) (P ∨ q) ∧ (p ∨ ~ q) = p ∨ (q ∨ ~ q) = P ∨ f = p

(iv) (P ∨ q) ∨ (p ∧ ~ q)

p	q	~ q	P ∨ q	p ∨ ~ q	(P ∨ q) ∧ (p ∨ ~ q),
T	T	F	T	F	T
T	F	T	T	T	T
F	T	F	T	F	T
F	F	T	F	F	F

(P ∧ q) ∧ (p ∨ ~ q)

p	q	~ q	P ∧ q	p ∧ ~ q	(P ∨ q) ∧ (p ∨ ~ q),
T	T	F	T	T	T
T	F	T	F	T	F
F	T	F	F	F	F
F	F	T	F	F	F

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Let (i) (P ∨ q) ∨ (p ∨ ~ q), (ii) (P ∧ q) ∧ (p ∨ ~ q), (iii) (P ∨ q) ∧ (p ∨ ~ q), (iv) (P ∨ q) ∨ (p ∧ ~ q), which one is tautology(1) (i)(2) (ii)(3) (iii)(4) (iv)

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