Maharashtra State BoardHSC Arts 12th Board Exam
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Write the negation of the following. If it is raining then we will go and play football. - Mathematics and Statistics

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Sum

Write the negation of the following.

If it is raining then we will go and play football.

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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.

Concept: Negations of Compound Statements
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