The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains. To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain.
If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true. In the above example, since the hypothesis and conclusion are equivalent, all four statements are true. But this will not always be the case! Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.
What if today was Tuesday. Tuesday is a weekday. So not every weekday is Monday. So the statement here is not true. The converse is not true.
Let's look at one more and apply it to geometry. If an angle measures 88 degrees, then it is acute. That's true by definition an acute angle is any angle that measures less than 90 degrees but more than 0 degrees. So let's find our converse. So I'm going to take the if, and instead of saying if an angle measures 88 degrees, I'm going to take the second part of this statement. So I'm going to write that instead of saying if it's acute, doesn't tell me anything, if an angle is acute, okay.
So there I had to add in a couple of words to make sure it made sense. Then now I'm going to say the second part. The angle measures 88 degrees. Then the angle measures 88 degrees. So if we look at this statement, let's say I had an angle right here that measured 75 degrees. However, a square is a special type of rectangle that has four sides of equal length. In summary, the original statement is logically equivalent to the contrapositive, and the converse statement is logically equivalent to the inverse.
That is a lot to take in! The statement is:. Now, pause the video and see if you can figure out the converse, inverse, and contrapositive statements. Remember, it helps to first turn our original statement into a conditional statement so you know the hypothesis and conclusion.
Here are the converse, inverse, and contrapositive statements based on the hypothesis and conclusion:. For example, If it is snowing, then it is cold. The logic structure of conditional statements is helpful for deriving converse, inverse, and contrapositive statements. What is the inverse statement of the following conditional statement? If it is snowing, then it is cold. An inverse statement assumes the opposite of each of the original statements.
What is the contrapositive statement for the following conditional statement? If it is a triangle, then it is a polygon. A contrapositive statement occurs when you switch the hypothesis and the conclusion in a statement, and negate both statements.
In this example, when we switch the hypothesis and the conclusion, and negate both, the result is: If it is not a polygon, then it is not a triangle. Identify p hypothesis and q conclusion in the following conditional statement.
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