Converse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.
Converse. Switching the hypothesis and conclusion of a conditional statement. For example, the converse of "If it is raining then the grass is wet" is "If the grass is wet then it is raining." Note: As in the example, a proposition may be true but have a false converse.
Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.
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. The negation of a statement simply involves the insertion of the word “not” at the proper part of the statement.
So a converse is not always true. So let's look at two examples. Here we're being asked find the converse of the statement, then ask yourself is it true. So this first statement says if it is Monday, then it is a weekday. Well, that's true. If today's Monday then it's a weekday. So the converse is going to take the if and the then and switch them.
A converse is when you switch the hypothesis and the conclusion. Original statement: If an number is even (Hypothesis) then it is divisible by two (Conclusion). This is a true statement. Converse statement: If a number is divisible by two (new Hyp...
About Mathematics. As a Converse Mathematics student, you’ll hone your critical thinking, reasoning, and logic skills, in addition to becoming adept with a wide range of computations and proofs. You’ll learn to question all assumptions and carefully assess claims. The tools you’ll learn to wield in the math program will make you a valuable asset to a variety of disciplines and industries.
The converse in geometry applies to a conditional statement. In a conditional statement, the words "if" and "then" are used to show assumptions and conclusions that are to be arrived at using logical reasoning. This is often used in theorems and problems involving proofs in geometry.
Keep the following two examples in mind as you study this lesson. Consider the true implication: “If it is raining, then the ground is wet.”
Contrapositive. Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."