Let p and q represent the following simple statements.
P: You eat your vegetables.
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.