UGC-NET | UGC NET CS 2016 Aug – II | Question 2

Let us assume that you construct ordered tree to represent the compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q). Then, the prefix expression and post-fix expression determined using this ordered tree are pgiven as ____ and _____ respectively.
(A) ↔~∧pq∨ ~ ~ pq, pq∧~p~q~∨↔
(B) ↔~∧pq∨ ~ p~q, pq∧~p~q~∨↔
(C) ↔~∧pq∨ ~ ~ pq, pq∧~p~~q∨↔
(D) ↔~∧pq∨ ~ p~ q, pq∧~p~ ~q∨↔


Answer: (B)

Explanation:
We have compound proposition (~ (p ∧ q)) ↔ (~ p ∨ ~ q):
Now we will construct ordered tree:

We are asked to determine pre-order (i.e. parent-node left-node right-node), we will drive it from ordered tree i.e. ↔ ~ ∧ p q ∨ ~ p ~q
And post-order(i.e. left-node right-node parent-node) from the ordered tree it is p q ∧ ~ p ~ q ~ ∨ ↔.
So, option (B) is correct.

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