Let 𝑝 and π‘ž be the following propositions: 𝑝: Fail grade can be given. π‘ž:…

2024

Let 𝑝 and π‘ž be the following propositions:

𝑝: Fail grade can be given.

π‘ž: Student scores more than 50% marks.

Consider the statement: β€œFail grade cannot be given when student scores more than 50% marks.”

Which one of the following is the CORRECT representation of the above statement in propositional logic?

  1. A.

    π‘ž β†’ Β¬ 𝑝

  2. B.

    π‘ž β†’ 𝑝

  3. C.

    𝑝 β†’ π‘ž

  4. D.

    Β¬ 𝑝 β†’ π‘ž

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Show answer & explanation

Correct answer: A

Correct representation: q β†’ Β¬p

  • Interpretation: p means "Fail grade can be given" and q means "Student scores more than 50% marks."

  • The sentence says that whenever q holds (student scores >50%), a fail cannot be given (Β¬p). So it is the implication q β†’ Β¬p.

  • Note: An equivalent form is the contrapositive p β†’ Β¬q, but the direct and clearest translation of the given sentence is q β†’ Β¬p.

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