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 difficult and I study hard but I shall not pass.
