Write the converse inverse and contrapositive of the statement

Conditional statements make appearances everywhere. What is also important are statements that are related to the original conditional statement by changing the position of PQ and the negation of a statement.

Given an if-then statement "if p , then q ," we can create three related statements:. To form the converse of the conditional statement, interchange the hypothesis and the conclusion. 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.

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. If we know that a statement is true or false , then we can assume that another is also true or false.

Example 2: Statement If a quadrilateral is a rectangle, then it has two pairs of parallel sides. The first step is to identify the hypothesis and conclusion statements. A careful look at the above example reveals something.

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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.

Write the converse inverse and contrapositive of the statement

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.

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These choices will be signaled to our partners and will not affect browsing data. A contrapositive statement occurs when you switch the hypothesis and the conclusion in a statement, and negate both statements. This declarative statement could also be referred to as a proposition. As can be seen in the diagram above, squares are a type of rectangle and a rectangle is a type of polygon. We also see that a conditional statement is not logically equivalent to its converse and inverse. Question 5: Which item shows the math statements matched with the correct logic symbols? Cite this Article Format. Example 1: Statement If two angles are congruent, then they have the same measure. However, a square is a special type of rectangle that has four sides of equal length. Transcript Practice Hi, and welcome to this video on mathematical statements! Hypothesis : a figure is a square Conclusion : the figure is a rectangle. Use limited data to select advertising. Understand audiences through statistics or combinations of data from different sources.

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 polygon, then it is not a triangle. Now we can use the definitions that we introduced earlier to create the three other statements. In the above example, since the hypothesis and conclusion are equivalent, all four statements are true. List of Partners vendors. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains. If a figure is a triangle, then it has three angles. Inverse If not p , then not q. The logic structure of conditional statements is helpful for deriving converse, inverse, and contrapositive statements. Create profiles to personalise content. If two angles have the same measure, then the two angles are congruent. Contrapositive proofs work because if the contrapositive is true, due to logical equivalence, the original conditional statement is also true. The first step is to identify the hypothesis and conclusion statements. Contrapositive If two angles do not have the same measure, then they are not congruent.