## Problem 1063

For the statement below, write the statement symbolically using parentheses and determine whether that statement is a negation, conjunction, dis-junction, conditional, or bi-conditional.

Statement:  If I don’t have to pay or I have enough money, then I can eat in the restaurant.

Solution:-

a. First break the compound statement down into its simple statements.

p: I have to pay.

q: I have enough money.

r: I can eat at the restaurant.

The comma indicates that the preceding portion of the compound statement should be placed in parentheses.

The word “or” indicates that the symbol v will be used.

The words “if” and “then” indicate that this is a conditional statement with r as the consequent and that the symbol → will be used.

The statement “I don’t have to pay” is the negative of the simple statement “I have to pay ” and is thus represented symbolically as ~p.

The “or” connective is in between the ~p and q statements, and that is represented as ~p v q.

If you combine all of these, you obtain (~p v q)→ r.

b.To determine whether the statement (~p v q) → r is a negation, conjunction, dis-junction, conditional, or bi-conditional, look at the symbol outside of the parentheses.

The → connective is outside the parentheses, so this indicates that the compound statement is a conditional.