Contraposition or Transposition of Conditional Proposition Contact

Which of the following is true regarding the contraposition of a conditional proposition?

Both propositions are negated

How is the converse of a conditional proposition obtained?

By swapping the hypothesis with the conclusion

Given that p is true and q is false, what are the truth values of p → q and its inverse?

False, True

Consider the conditional proposition: If Alaska is one of the original 13 states, then 7 < 8. Which of the following is its converse?

If 7 < 8, then Alaska is one of the original 13 states

How would the contraposition of the conditional proposition of "If it is a hot day, then we turn the air conditioner on" be stated?

If the air conditioner is not on, then it is not a hot day

If a conditional proposition is true, what will be the truth value of the inverse?

It can be either true or false

Which of the following is true about the inverse of a conditional proposition, p → q?

It is written as ¬p → ¬q

What can be the value of the converse of the conditional proposition p → q if it is true?

It may not be the same as the value of the conditional proposition

Which of the following indicates a difference between the converse and contraposition of a conditional proposition?

The propositions are negated in contraposition

Which of the following is true of the converse and the inverse of a conditional proposition?

They always have the same truth value

What are the truth values of the conditional proposition, p → q, and its converse given that p is false and q is false?

True, True

If the conditional proposition is p → q, what is its converse?

q → p

If the conditional proposition is p → q, what is it contraposition?

¬q → ¬p