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17/01/2022 2:31 pm
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The Boolean expression (p ∧ q) ⇒ ((r ∧ q) ∧ p) is equivalent to
(1) (p ∧ q) ⇒ (r ∧ q)
(2) (q ∧ r) ⇒ (p ∧ q)
(3) (p ∧ q) ⇒ (r ∨ q)
(4) (p ∧ r) ⇒ (p ∧ q)
1 Answer
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17/01/2022 2:43 pm
Correct answer: (1) (p ∧ q) ⇒ (r ∧ q)
Explanation:
(p ∧ q) ⇒ ((r ∧ q) ∧ p) ∼ (p ∧ q) ∨ ((r ∧ q) ∧ p) ∼ (p ∧ q) ∨ (r ∧ q) ∧ (p ∧ q)
⇒ [∼ (p ∧ q) ∨ (p ∧ q)] ∧ (∼(p ∧ q) ∨ (r ∧ p))
⇒ t ∧ [∼ (p ∧ q) ∨ (r ∧ p)
⇒ ∼ (p ∧ q) ∨ (r ∧ q)
⇒ (p ∧ q) ⇒ (r ∧ q)
Alternate:
given statement says
"if p and q both happen then
p and q and r will happen"
it Simply implies
"If p and q both happen then 'r' too will happen "
i.e. "if p and q both happen then r and p too will happen
i.e. (p ∧ q) ⇒ (r ∧ q)