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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

Expert verified

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

Step by step solution

01

Step 1. Given Information.

A statement:

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

02

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 " .

03

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.

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