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GATE Overflow Test Series | Mock GATE | Test 5 | Question: 28

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Anjana, Chandani, and Pooja are three students that took the Logic exam. Let’s consider a propositional language where $p$ represents “Anjana passed the exam”, $q$ represents “Chandani passed the exam” and $r$ represents "Pooja passed the exam".

Which of the following is the formal representation of the sentence “At least two among Anjana, Chandani and Pooja passed the exam”?

  1. $p \vee q \vee r$
  2. $p \wedge q \wedge r$
  3. $(p \wedge q \wedge \neg r )\vee (\neg p \wedge q \wedge r)\vee (p \wedge \neg q \wedge r)$
  4. None of the above
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"At least" two also include all three. So, option C is false. The correct expression should be $(p \wedge  q  )\vee ( q \wedge  r)\vee (p \wedge  r).$
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