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.
A statement that can be written in if-then form is called Conditional Statement. The phrase immediately following the word if is the hypothesis. The phrase immediately following the word then is the conclusion. Statements that have the same truth values are logically equivalent. They are either both.Write the converse, inverse, and contrapositive of the following conditional statement. Of these four propositions, state which pairs are logically equivalent. 6. If Jose has a family, then he has a father. Converse Inverse Contrapositive.Write the a. converse, b. inverse, and c. contrapositive of the given statement. In a right triangle, the acute angles are complementary.
The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
Conditional Statements. Author: Robert Sharpe. Conditional Statement Practice. For the following conditional statement write it's converse, inverse and contrapositive and state the truth value for each. Converse. What is the converse to the following conditional statement? If there is lightning, then practice is canceled. Check your answer here. If there is not lightening, then practice is not.
Consider the following conditional statement: “If, then ”. Write the converse, the inverse, and the contrapositive of the above statement. When possible, classify the statement as true or false.
Write the converse, inverse and contrapositive for the statement below. If the segment has a midpoint, then it is bisected. A: Converse: If the segment is bisected, then it has a midpoint. Inverse: If the segment doesn't have a midpoint, then it isn't bisected. Contrapositive: If the segment isn't bisected, then it doesn't have a midpoint. Write the biconditional statment of the following and.
Read the following conditional statement: If it is raining, then Amelia has her umbrella up. Write the converse of the statement. Write the inverse of the statement. Write the contrapositive of the statement. Here, we have our statement: “If it is raining, then Amelia has her umbrella up.” This is an if-then statement. If it is raining.
The logical converse and inverse of the same conditional statement are logically equivalent to each other. The Contrapositive Okay, enough with the warm-up, now it's time to get really weird.
Example 3: Examining the relationship between the converse and inverse of a conditional statement (p. 212) Arizona is studying the colour wheel in art class. She observes the following: “If a colour is red, yellow, or blue, then it is a primary colour.” a) Write the converse of this statement. b) Write the inverse of this statement.
For each of the following, rewrite the original conditional statement in if-then form if necessary. Then, write the converse, inverse, and contrapositive of each. Finally, determine the truth value of each and provide a counterexample for each false statement. 1. If you are a quarterback, then you play football T or F Converse: T or F Inverse: T or F Contrapositive: T or F 2. The sum of two.
Converse, Inverse, and Contrapositive Learning Targets: the truth value of the converse, inverse, and contrapositive of a conditional statement. rite and nter re iconditional statements. Vocabulary Organizer, SUGGESTED LEARNING STRATEGIES: Interactive Word Wall, Think-Pair-Share, Group Presentation, Discussion Groups Every conditional statement has three related conditionals. These are the.
Write the (a) inverse, (b) converse, and (c) contrapositive of the statement. If there is snow on the ground, then flowers are not in bloom. When two statements are both true or both false, they are called equivalent statements. A conditional statement is equivalent to its contrapositive. Similarly, the inverse and converse of any conditional.
Got It? 4. What are the converse, inverse, and contrapositive of the conditional statement below? What are the truth values of each? If a statement is false, give a counterexample. If a vegetable is a carrot, then it contains beta carotene. Below are the truth values of the related statements above. Equivalent statements have the same truth.
When two statements are both true or both false, they are called equivalent statements. A conditional statement is equivalent to its contrapositive. Similarly, the inverse and converse of any conditional statement are equivalent. This is shown above. Practice Questions. Question 1: Rewrite the following conditional statements in if-then form.
Write the converse, inverse, and contrapositve of each conditional statement. Determine if each related conditional is true or false. If a stament is false, provide a counterexample. Ex 1 If a polygon is a square, then it is a rectangle.
In this worksheet, we will practice analyzing a given statement to identify hypothesis and conclusion to write it in if-then form; writing its converse, inverse, and contrapositive; constructing the conditional truth table; representing it using a Venn diagram; or identifying negations, conjunctions, and disjunctions.