Question

Conditional: If it is January, then there are 31 days this month. For the given conditional statement, determine which of the following option(s) has a truth value of true. Select all that apply. Conditional Converse Inverse Contrapositive

Answer 1

If it's January then 31 days/month.
conditional p --> q
TRUE - January has 31 days/month

converse q --> p
If there's 31 days/month then it's January
FALSE - October has 31 days

Inverse ~p --> ~q
if it's not January then it's not 31 days/month
FALSE - It could be October or December which have 31 days/month

Contrapositive ~q --> ~p
If there's not 31 days/month then it's not January.
TRUE - January must have 31 days/month

Answer 2

Answer:

The converse of the conditional switches the hypothesis with conclusion portion of the statement.

The inverse of the conditional negates both the hypothesis and the conclusion portions of the statement .

The contrapositive  of the conditional statement combines the converse with the inverse and switches the hypothesis and conclusion while negating both portions.

It is a conditional statement.(if p then q form) - True

The converse is not true. As converse is - If there are 31 days in a month, then it is January. It is not true as March and other months also have 31 days.

The inverse is false. As inverse is - If it is not January, then there are not 31 days this month. This also holds true for January only but many other months also have less than 31 days.

The contrapositive is true . As the statement forms : If there are not 31 days this month, then it is not January. This holds true.