Question

Let​ p, q, and r represent the following simple statements.

​p:	It is snowing outside
​q:	It is cold
​r:	It is cloudy.

Write the following compound statement in its symbolic form.

If

it is snowing outside

then

it is cold

or

it is not cloudy

Answer 1

p : It is snowing outside

q : It is cold

r : It is cloudy

Given compound statement : If it is snowing outside then it is cold or it is not cloudy

The corresponding symbolic form : p -> (r ∨ ~q)

Explanations :

1. "If p then q" is denoted symbolically by "p -> q"; p is called the hypothesis and q is called the conclusion.

2. "Not q" is represented symbolically by "~q"

3. "p or q" is represented symbolically as "p ∨ q"

The given statement is thus formed by combining all the three explanations as given.