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Mathematical Logic — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMathematical Logic2 Marks
MCQ
Which of the following statement is contradiction?
  • A
    $(p \wedge q) \rightarrow q$
  • ✓
    $(p \wedge \sim q) \wedge(p \rightarrow q)$
  • C
    $p \rightarrow \sim(p \wedge \sim q)$
  • D
    $(p \wedge q) \vee \sim q$
✓

Answer

Correct option: B.
$(p \wedge \sim q) \wedge(p \rightarrow q)$
(B)
consider option (B)
$(p \wedge \sim q) \wedge(p \rightarrow q)$
$\equiv \sim(p \rightarrow q) \wedge(p \rightarrow q)$
$\equiv F \quad \ldots[$ Complement Law $]$

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