Hello to all.

In a routine exercise I have been given the following statement:

Let k be an integer, if k^2 is a multiple of 2, then k is a multiple of 2.I am then asked to determine the negative, converse, inverse and contrapositive of the aforementioned statement. The difficulty or doubt I am having is with the first portion of the statement (Let k be an integer...), specifically how or if it varies.

The following are the rules I used to determine my answers:

Starting with A=>B,

Negation: not (A=>B) is log.equiv. to (A and not B)

Converse: B=>A

Inverse: (not A) => (not B)

Contrapositive: (not B) => (not A)

With that in mind, the following are my findings:

Negation:

Let k be an integer, if k^2 is a multiple of 2 and k is not a multiple of 2.

Converse:

Let k be an integer, if k is a multiple of 2, then k^2 is a multiple of 2.

Inverse:

Let k be an integer, if k^2 is not a multiple of 2 then k is not a multiple of 2.

I wish to thank everyone in advance who offers help in determining if I am on the right path. Good day to all.

Contrapositive:

Let k be an integer, if k is not a multiple of 2 then k^2 is not a multiple of 2.