UGC-NET | UGC NET CS 2015 Jun – II | Question 8

“If my computations are correct and I pay the electric bill, then I will run out of money. If I don’t pay the electric bill, the power will be turned off. Therefore, if I don’t run out of money and the power is still on, then my computations are incorrect.”
Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where ¬ means NOT)

(A) if (c Λ b)→r and ¬b→p, then (¬r Λ p)→¬c
(B) if (c ∨ b)→r and ¬b→¬p, then (r Λ p)→c
(C) if (c Λ b)→r and ¬p→b, then (¬r ∨ p)→¬c
(D) if (c ∨ b)→r and ¬b→¬p, then (¬r Λ p)→¬c


Answer: (A)

Explanation: “If my computations are correct and I pay the electric bill, then I will run out of money.” : if (c Λ b)→r
“If I don’t pay the electric bill, the power will be turned off. Therefore, if I don’t run out of money and the power is still on, then my computations are incorrect.” : (¬r Λ p)→¬c .
So, option (A) is correct.

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