Question

given:

• let ( p ) represent \a shape is a rectangle\.
• let ( q ) represent \a shape has 4 right angles\.

what is the symbolic form of \if a shape is not a rectangle, then it does not have 4 right angles\?
( sim p \to sim q )
( p \to q )
( sim q \to sim p )
( q \to p )

Explanation:

Step1: Analyze the logical structure

The statement is "If a shape is not a rectangle, then it does not have 4 right angles".
The symbol for "not" is $\sim$. So "not \(p\)" is $\sim p$ and "not \(q\)" is $\sim q$.
The symbol for "if... then..." is $\to$.

Step2: Translate the statement

The structure "If \(A\), then \(B\)" is translated as \(A\to B\). Here \(A = \sim p\) and \(B=\sim q\). So the symbolic form is $\sim p\to\sim q$.

Answer:

$\sim p\to\sim q$ (the first option)