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