Write the converse inverse and contrapositive of the statement

Given an if-then statement "if pthen 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.

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

How to Prove the Complement Rule in Probability. Now we can define the converse, the contrapositive and the inverse of a conditional 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. 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.

Write the converse inverse and contrapositive of the statement

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. In this article, we will discuss all the things related to the Converse statement in detail. A converse statement is a proposition formed by interchanging the hypothesis and conclusion of a conditional statement. A converse statement is formed by exchanging the hypothesis and conclusion of a conditional statement while retaining the same meaning. To write a converse statement, you simply switch the hypothesis and conclusion of a conditional statement while maintaining the same meaning.

Jessica bartlett

As can be seen in the diagram above, squares are a type of rectangle and a rectangle is a type of polygon. Here are the converse, inverse, and contrapositive statements based on the hypothesis and conclusion:. An inverse statement assumes the opposite of each of the original statements. 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. Converse If a quadrilateral has two pairs of parallel sides, then it is a rectangle. Understand audiences through statistics or combinations of data from different sources. A careful look at the above example reveals something. 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. Conditional statements make this pretty easy, as the hypothesis follows if and the conclusion follows then. Study Guides Flashcards Online Courses. These, along with some reasoning skills, allow us to make sense of problems presented in math. It will help to look at an example. 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.

We can rewrite this statement using letters to represent the hypothesis and conclusion. The contrapositive is logically equivalent to the original statement.

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. When the hypothesis and conclusion are identified in a statement, three other statements can be derived:. Specifically, we will learn how to interpret a math statement to create what are known as converse, inverse, and contrapositive statements. An example will help to make sense of this new terminology and notation. The hypothesis is it is raining and the conclusion is grass is wet. If not p , then not q. Identify p hypothesis and q conclusion in the following conditional statement. However, a square is a special type of rectangle that has four sides of equal length. Which of the other statements have to be true as well? If we know that a statement is true or false , then we can assume that another is also true or false. Since a conditional statement and its contrapositive are logically equivalent, we can use this to our advantage when we are proving mathematical theorems. For example, If it is snowing, then it is cold.