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1.

What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard.1. The examination is difficult and I study hard but I shall not pass2. The examination is difficult and I study hard and I shall pass3. The examination is not difficult and I study hard and I shall pass4. None of these

Answer» Correct Answer - Option 1 : The examination is difficult and I study hard but I shall not pass

Concept:

Let p and q are any two statements.

\(\rm \sim (p \rightarrow q) = p \wedge q\)

Calculations:

Let p:The examination is difficult.

q:I shall pass.

r:I study hard.

Symbolic form of "If the examination is difficult, then I shall pass if I study hard." is\(\rm p \rightarrow (r \rightarrow q)\)

Symbolic form of Negation of "If the examination is difficult, then I shall pass if I study hard." =\(\rm \sim (\rm p \rightarrow (r \rightarrow q))\)

we know,

⇒\(\rm \sim (\rm p \rightarrow (r \rightarrow q))\)=\(\rm p \wedge (r \wedge \sim q)\)

Hence, the examination is difficultand I study hard but I shall not pass.
Discussion