Question

Write the negations of :

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

Answer 1

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.’