First slide

Introduction to mathematical reasoning

Question

What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard.

Moderate

A

The examination is difficult and I study hard but I shall not pass
B

The examination is difficult and I study hard and I shall pass
C

The examination is not difficult and I study hard and I shall pass
D

None of these

Solution

If p : Examination is difficult
q : I shall pass
r : I study hard
$Given result is p \Rightarrow (r \Rightarrow q)$
$Now, ~ (r \Rightarrow q) = r \land ~ q$
$~ (p \Rightarrow (r \Rightarrow q)) \equiv p \land (r \land ~ q)$
The examination is difficult and I study hard but I shall not pass.

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