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.