## Problem 1062

For the statement below, perform the following.

a. Write the statement symbolically by using parentheses.

b. Determine whether the statement is a negation is a negation, conjunction, dis-junction, conditional, or bi-conditional.

Statement: It is false that if your car is broken then you will not be late for work.

Solution:-

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

q: You will be late for work.

Recall that the symbol ‘→’ means “if-then” while the symbol ‘↔’ means “if and only if”. The symbol ‘~’ is used to negate a statement.

Notice that the statement is an “if-then” statement, the second simple statement is negate, and “it is false” represents a negation of the compound statement. Thus, the statement written symbolically is ~(p→~q).

b. Determine how to classify the given statement. Recall that the symbol ‘~’  means negation, the conditional is symbolized by ‘→’ , the bi-conditional is  symbolized by ‘↔’ , the bi-conditional is symbolized by ‘↔’, the symbol ‘Λ’ represents conjunctions, and ‘v’ represents dis-junctions. Look for the most dominant connective when trying to determine what kind of statement it is

Therefore , the statement found in part (a) is a negation.