Question

What is the contrapositive of the implication “If A, then B"?

Find the contrapositives of the following implications:

If a divides b and b dividesc, then a divides c.

Short answer

If a does not divide c, a does not divide b and b does no divide c.

Step-by-step solution

Step 1. Given Information.

A statement:

If a divides b and b dividesc, then a divides c.

Step 2. The contrapositive statement.

Definition of contrapositive:

A proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them "if not-B then not-A " is the contrapositive of "if A then B " .

Step 3. The contrapositive statement.

The contrapositive statement will be:

If a does not divide c, a does not divide b and b does no divide c.