Question

In: Statistics and Probability

For each statement in the referenced exercise write the converse, inverse, and contrapositive. Indicate as best...

For each statement in the referenced exercise write the converse, inverse, and contrapositive. Indicate as best as you can which among the statement, its converse, its inverse, and its contrapositive are true and which are false. Give a counterexample for each that is false.

∀ integers n,if n is divisible by 6, then n is divisible by 2 and n is divisible by 3.

Solutions

Expert Solution

Given statement is

integers if is divisible by , then is divisible by and is divisible by (TRUE)

Converse of the given statement is

integers if   is divisible by and is divisible by then   is divisible by (TRUE)

Inverse of the given statement is

integers if is not divisible by , then is not divisible by and is not divisible by (TRUE)

Contrapositive of given statement is

integers if   is not divisible by and is not divisible by then   is not divisible by (TRUE)

orchestra answered 3 years ago
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