JEE Previous Year Question
The Boolean expression (p ∧ q) ⇒ ((r ∧ q) ∧ p) is equivalent to:
Topic: JEE PYQ
Answer: A. Full step-by-step solution below.
- A(p ∧ q) ⇒ (r ∧ q)
- B(q ∧ r) ⇒ (p ∧ q)
- C(p ∧ q) ⇒ (r ∨ q)
- D(p ∧ r) ⇒ (p ∧ q)
Correct answer: A
Solution
(a)(p ∧q) ⇒ ((r ∧q) ∧p)
∼ (p ∧q) ∨ ((r ∧q) ∧p)
∼ (p ∧q) ∨ ((r ∧p) ∧ (p ∧q)
⇒ [∼ (p ∧q) ∨ (p ∧q)] ∧ (∼ (p ∧q) ∨ (r ∧p))
⇒t ∧ [∼ (p ∧q) ∨ (r ∧p)]
⇒∼ (p ∧q) ∨ (r ∧p)
⇒ (p ∧q) ⇒ (r ∧p)
Aliter :
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 and both happen then r and p too will happen
i.e. (p ∧q) ⇒ (r ∧p)