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Mathematical Reasoning
medium
Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard
A
The examination is difficult and I study hard and I shall pass
B
The examination is difficult and I study hard but I shall not pass
C
The examination is not difficult and I study hard and I shall pass
D
None of these
Solution
(b) $p :$ examination is difficult,
$q :$ I shall pass,
$r :$ I study hard
Given result is : $p \Rightarrow (r \Rightarrow q)$
Now $\sim(r \Rightarrow q)$ $= r \wedge \sim q$
$\sim(p \Rightarrow (r \Rightarrow q)) \equiv p \wedge (r\; \wedge \sim\,q)$
The examination is difficult and I study hard but I shall not pass.
Standard 11
Mathematics
