## Problem 1054

Let p and q represent the following simple statements.

q: You get dessert.

Write the following compound statement in its symbolic form.

If you do not eat your vegetables, than you do not get dessert.

Solution:-

The given compound statement is a conditional statement.

A conditional statement is a compound statement formed by joining two statements with the connective if-then.

“You do not eat your vegetables” is the first simple statement in the conditional; it follows the word if.

Since this statement is the negation of the statement represented by p, its symbolic form is ~p.

“You do not get dessert” is the second simple statement in the conditional; it follows the word then.

Since this statement is the negation of the statement represented by q, its symbolic form is ~q.

The symbol that represents the connective if-then is →.

Note symbol the words “if” and “then” do not have separate symbols. A single symbol represents the connective if-then.

To write the conditional statement in symbolic form, begin by replacing the first simple statement with its symbolic form. Then, replace the connective if-then by the symbol that represents it. Finally, write the second simple statement in symbolic form.

If you do not eat your vegetables,   then  you do not get dessert.

~p                         →                         ~q

The symbolic form for the given conditional statement is

~p→~q.