Write the converse inverse and contrapositive of the statement

Given an if-then statement "if pthen q ," we can create three related statements:.

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.

Write the converse inverse and contrapositive of the statement

Hi, and welcome to this video on mathematical statements! Specifically, we will learn how to interpret a math statement to create what are known as converse, inverse, and contrapositive statements. These, along with some reasoning skills, allow us to make sense of problems presented in math. This declarative statement could also be referred to as a proposition. Two independent statements can be related to each other in a logic structure called a conditional statement. When the hypothesis and conclusion are identified in a statement, three other statements can be derived:. An example will help to make sense of this new terminology and notation. The first step is to identify the hypothesis and conclusion statements. Conditional statements make this pretty easy, as the hypothesis follows if and the conclusion follows then. The hypothesis is it is raining and the conclusion is grass is wet. Now we can use the definitions that we introduced earlier to create the three other statements. How is this helpful? The key is in the relationship between the statements.

Two independent statements can be related to each other in a logic structure called a conditional statement. This declarative statement could also be referred to as a proposition. Popular Cities.

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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.

Write the converse inverse and contrapositive of the statement

We can rewrite this statement using letters to represent the hypothesis and conclusion. The contrapositive is logically equivalent to the original statement. The converse and inverse may or may not be true. When the original statement and converse are both true then the statement is a biconditional statement. What if you were given a conditional statement like "If I walk to school, then I will be late"? Find the converse, inverse, and contrapositive. Determine if each resulting statement is true or false. If it is false, find a counterexample. The original statement is true. If I am at Disneyland, then I am in California.

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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. Return to Basic Arithmetic Videos. Contrapositive If not q , then not p. Converse, Inverse, and Contrapositive. We will examine this idea in a more abstract setting. Measure content performance. Taylor, Courtney. Inverse If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. However, a square is a special type of rectangle that has four sides of equal length. Learn about our Editorial Process. Measure advertising performance. If a quadrilateral is not a rectangle, then it does not have two pairs of parallel sides. If it is snowing, then it is cold. Contrapositive If two angles do not have the same measure, then they are not congruent.

Converse Statement is a type of conditional statement where the hypothesis or antecedent and conclusion or consequence are reversed relative to a given conditional statement.

If it is not a triangle, then it is not a polygon. Question 4: Identify p hypothesis and q conclusion in the following conditional statement. Taylor, Courtney. If it is snowing, then it is cold. Converse If a quadrilateral has two pairs of parallel sides, then it is a rectangle. A careful look at the above example reveals something. If a quadrilateral has two pairs of parallel sides, then it is a rectangle. Because the conditional statement and the contrapositive are logically equivalent, we can assume the following to be TRUE:. But this will not always be the case! Study Guides Flashcards Online Courses. If two angles have the same measure, then the two angles are congruent. If the statement is true, then the contrapositive is also logically true. Two independent statements can be related to each other in a logic structure called a conditional statement. The key is in the relationship between the statements. Contradictory Premises in an Argument.