Let p and q denote the following statements p: The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is

Question

Let p and q denote the following statements p: The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is (A) q ⇒ ∼ p (B) q ∧ ∼ p (C) p ∧ ∼ q (D) ∼ q ⇒∼ p

Tardigrade Admin · Accepted Answer

Let p: The sun is shining. q: I shall play tennis in the afternoon. Negation of p → q is ∼(p → q) = p ∧∼ q

Q. Let p and q denote the following statements
p : The sun is shining
q: I shall play tennis in the afternoon
The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is

$q \Rightarrow\sim p$

$q \land \sim p$

$p \land \sim q$

$\sim q \Rightarrow\sim p$

Let p : The sun is shining.
q : I shall play tennis in the afternoon.
Negation of $p \to q$ is $\sim (p \to q) = p \land \sim q$

Q. Let p and q denote the following statements p : The sun is shining q: I shall play tennis in the afternoon The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is

q⇒∼p

q∧∼p

p∧∼q

∼q⇒∼p