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Question 3Asked in UGC NET Computer Science, June 2015 (Paper II & III, Selected Questions)

"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.…

"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)
  1. Aif (c ∧ b) → r and ¬b → ¬p, then (¬r ∧ p) → ¬c
  2. Bif (c ∧ b) → r and ¬b → ¬p, then (r ∧ p) → c
  3. Cif (c ∧ b) → r and ¬p → ¬b, then (¬r ∧ p) → ¬c
  4. Dif (c ∨ b) → r and ¬b → ¬p, then (¬r ∧ p) → ¬c
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Correct answer: (A) if (c ∧ b) → r and ¬b → ¬p, then (¬r ∧ p) → ¬c

Explanation

S₁: (c ∧ b) → r S₂: ¬b → ¬p Conclusion: (¬r ∧ p) → ¬c So: if (c ∧ b) → r and ¬b → ¬p, then (¬r ∧ p) → ¬c.

From UGC NET Computer Science PYQ, June 2015 (Paper II & III, Selected Questions)

This is question 3 of UGC NET Computer Science PYQ, June 2015 (Paper II & III, Selected Questions). See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.