Use the conditional statement to answer the question.

If today is Thursday, then tomorrow is Friday.

What is the inverse of the statement?

If tomorrow is Friday, then today is Thursday.

If tomorrow is not Friday, then today is not Thursday.

If today is not Thursday, then tomorrow is Friday.

If today is not Thursday, then tomorrow is not Friday.

Use the conditional statement to answer the question.

If an angle is a right angle, then the angle measures 90°.

Are the statement and its contrapositive true?

Both the statement and its contrapositive are false.

The statement is false, but the contrapositive is true.

Both the statement and its contrapositive are true.

The statement is true, but the contrapositive is false.

Use the conditional statement to answer the question.

If today is Monday, then yesterday was Sunday.

Can the statement be written as a biconditional statement and why?

No, because the statement is true, but its converse is false

No, because the statement is false, but its converse is true

Yes, because the statement and its converse are both true

No, because the statement and its converse are both false

1) Let be a proposition of the form [tex]p \implies q[/tex], where [tex]p[/tex] and [tex]q[/tex] are simple propositions and the logical connector is a implication. The inverse of the proposition is defined by:

[tex]\lnot p\implies \lnot q[/tex] (1)

Which is not logically equivalent to the original proposition.

If [tex]p : =[/tex] today is Thursday and [tex]q :=[/tex] tomorrow is Friday, then the inverse of the statement is:

If today is not Thursday, then tomorrow is not Friday.

Then, we conclude that the inverse of the statement is If today is not Thursday, then tomorrow is not Friday.

2) Let be a proposition of the form [tex]p \implies q[/tex], where [tex]p[/tex] and [tex]q[/tex] are simple propositions and the logical connector is a implication. The contrapositive of the proposition is defined by:

[tex]\lnot q \implies \lnot p[/tex]

If [tex]p:=[/tex] an angle is a right angle and [tex]q :=[/tex] the angle measures 90°, then the original statement and its contrapositive are:

Original statement

If an angle is a right angle, then the angle measures 90°.

Both the antecedent and consequent are true. Hence, original statement is also true.

Contrapositive

If the angle does not measure 90°, then an angle is not a right angle.

Both the antecedent and consequent are false. Hence, contrapositive is also false.

Hence, the correct choice is: Both the statement and its contrapositive are true.

3) In a implication, a proposition is false when its antecedent is true and its consequent is false. If both propositions are true, then [tex]p \implies q \,\land\,q \implies p[/tex] by Principle of Addition, which is equivalent to [tex]p\iff q[/tex].

Hence, the correct choice is: Yes, because the statement and its converse are both true.

We kindly invite to check this question on propositions: https://brainly.com/question/2321704