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Question
Write the negation of the following.
If it is raining then we will go and play football.
Solution
Let p: It is raining.
q: We will go.
r: We play football.
Then the symbolic form of the given statement is p → (q ∧ r).
Since ∼ [p → (q ∧ r)] ≡ p ∧ ∼ (q ∧ r) ≡ p ∧ (∼ q ∨ ∼ r), the negation of the given statement is:
It is raining and we will not go or not play football.
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