Chapter 9, Problem 10CT

To determine

To write if-then form, the converse, the inverse, the contrapositive, and the biconditional of the given conditional statement.

Answer to Problem 10CT

If-then form conditional statement:

If relation is a function then each input has exactly one output.

The converse of a conditional statement:

If each input has exactly one output then relation is a function

The inverse conditional statement:

If relation is not a function then each input does not have exactly one output.

The contrapositive conditional statement:

If each input does not have exactly one output then relation is not a function.

The biconditional of the conditional statement:

Relation is a function if and only if each input has exactly one output.

Explanation of Solution

Given information:

The conditional statement given is

A relation that pairs each input with exactly one output is a function

Concept used:

If-then form conditional statement:

When a conditional statement is written if-then form the “if” part contains the hypothesis and the “then” part contains the conclusion.

The converse of a conditional statement:

To write the converse of a conditional statement, exchange the hypothesis and the conclusion.

The inverse conditional statement:

To write the inverse of a conditional statement, negate both the hypothesis and the conclusion.

The contrapositive conditional statement:

To write the contrapositive of a conditional statement, first write the converse. Then negate both the hypothesis and the conclusion.

The biconditional of the conditional statement:

When a conditional statement and its converse both are true, it can be written as a single statement using phrase “if and only if” it is called biconditional statement.

If-then form conditional statement:

If relation is a function then each input has exactly one output.

The converse of a conditional statement:

If each input has exactly one output then relation is a function

The inverse conditional statement:

If relation is not a function then each input does not have exactly one output.

The contrapositive conditional statement:

If each input does not have exactly one output then relation is not a function.

The biconditional of the conditional statement:

Relation is a function if and only if each input has exactly one output.