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GATE 2014 CS (CS1) – Question 63

Engineering Mathematics · Discrete Mathematics: Propositional and First Order Logic · 2 marks · Multiple choice

Which propositional formula is TRUE exactly when two of p, q, r are TRUE?

  1. $((p\leftrightarrow q)\land r)\lor(p\land q\land\neg r)$
  2. $(\neg(p\leftrightarrow q)\land r)\lor(p\land q\land\neg r)$
  3. $((p\to q)\land r)\lor(p\land q\land\neg r)$
  4. $(\neg(p\leftrightarrow q)\land r)\land(p\land q\land\neg r)$

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Show answer and explanation

Correct answer: (B) $(\neg(p\leftrightarrow q)\land r)\lor(p\land q\land\neg r)$

Explanation

When r is true, exactly one of p,q must be true, represented by¬(p↔q)∧r. When r is false, both p,q must be true, represented by p∧q∧¬r. Their disjunction is **B** and accepts precisely110,101,011.