Chapter 6, Problem 1RE

Determine whether each of the following statements is true or false, and explain why.

1. A compound statement is a negation, a conjunction, a disjunction, a conditional, or a biconditional.

To determine

Whether the statement “A compound statement is a negation, a conjunction, a disjunction, a conditional, or a bi conditional” is true or false and explain the reason.

Answer to Problem 1RE

The statement is true.

Explanation of Solution

Definition used:

When one or more simple statements are combined with logical connectives such as and, or, not, and if $\dots$ then, the result is called a compound statement, while the simple statement that make up the compound statement are called component statements.

Description:

A negation of a true statement is false, and the negation of a false statement is true. In this case the logical connective ‘not’ is being used and hence that statement can be considered as a compound statement.

A conjunction, a disjunction, a conditional, or a bi conditional is also statements that are combined by logical connectives ‘and’, ‘or’, ‘if $\dots$ then’ and ‘if and only if’, respectively.

Hence, these statements are also compound statements.

Therefore, the given statement is true.