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GATE CS 2024 Set 2 — Question 12

MCQ+1 / -0.33EasyPropositional LogicMathematical LogicEngineering Mathematics

Engineering Mathematics → Mathematical Logic → Propositional Logic

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Question

Let pp and qq be the following propositions:
pp: Fail grade can be given.
qq: Student scores more than 50% marks.
Consider the statement: "Fail 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?
A.
q→¬pq \rightarrow \neg p
B.
q→pq \rightarrow p
C.
p→qp \rightarrow q
D.
¬p→q\neg p \rightarrow q

Correct answer

(A) q arrow ¬ p

Solution

The statement is "Fail grade cannot be given when student scores more than 50% marks."
This can be rephrased as an implication: "If a student scores more than 50% marks, then a fail grade cannot be given."
  • "Student scores more than 50% marks" corresponds to proposition qq.
  • "Fail grade can be given" corresponds to proposition pp.
  • "Fail grade cannot be given" corresponds to ¬p\neg p.
Thus, the implication is q→¬pq \rightarrow \neg p.

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