Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false.
-If 10 does not divide the counting number, then 5 does not divide the counting number.
A) If 5 divides the counting number, then 10 divides the counting number. true
B) If 10 divides the counting number, then 5 divides the counting number. true
C) If 10 divides the counting number, then 5 divides the counting number. false
D) If 5 divides the counting number, then 10 divides the counting number. false

Question

Quizplus · Accepted Answer

The contrapositive of a statement "If P, then Q" is "If not Q, then not P". The original statement is "If 10 does not divide the counting number, then 5 does not divide the counting number." The contrapositive is "If 5 divides the counting number, then 10 divides the counting number." This statement is false because a number can be divisible by 5 without being divisible by 10 (e.g., 5, 15, 25, etc.).

Write the Contrapositive of the Statement