Need even more definitions? Homophones, Homographs, and Homonyms The same, but different. Merriam-Webster's Words of the Week - Nov. Ask the Editors 'Everyday' vs. What Is 'Semantic Bleaching'? How 'literally' can mean "figuratively".
Literally How to use a word that literally drives some pe Is Singular 'They' a Better Choice? The awkward case of 'his or her'. Example 2: Statement If a quadrilateral is a rectangle, then it has two pairs of parallel sides.
Converse If a quadrilateral has two pairs of parallel sides, then it is a rectangle. Inverse If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. Contrapositive If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle.
Subjects Near Me. Download our free learning tools apps and test prep books. Varsity Tutors does not have affiliation with universities mentioned on its website. If not p , then not q. If not q , then not p.
If a quadrilateral has two pairs of parallel sides, then it is a rectangle. Conditional statements make appearances everywhere. What is also important are statements that are related to the original conditional statement by changing the position of P , Q and the negation of a statement. Starting with an original statement, we end up with three new conditional statements that are named the converse, the contrapositive, and the inverse. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation.
Every statement in logic is either true or false. It will help to look at an example. We will examine this idea in a more abstract setting.
Now we can define the converse, the contrapositive and the inverse of a conditional statement. We will see how these statements work with an example. We may wonder why it is important to form these other conditional statements from our initial one. A careful look at the above example reveals something. Which of the other statements have to be true as well? What we see from this example and what can be proved mathematically is that a conditional statement has the same truth value as its contrapositive.
We say that these two statements are logically equivalent. We also see that a conditional statement is not logically equivalent to its converse and inverse. Since a conditional statement and its contrapositive are logically equivalent, we can use this to our advantage when we are proving mathematical theorems. Contrapositive proofs work because if the contrapositive is true, due to logical equivalence, the original conditional statement is also true.
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