Converses, contrapositives and proof by the contrapositive the converse of the implication p q is the reverse implication q p. If a conditional is false then the converse is false. Converse inverse contrapositive worksheets printable. Variations on the conditional statement direct statement converse inverse contrapositive if p, then q. Worksheets are unit 4 logic packet, logic and conditional statements, lesson practice a conditional statements, conditional statements, geometry, geometry, converse and contrapositive work 3. If you didnt pass the test, then you didnt study for the test. A conditional statement consists of two parts, a hypothesis in the if clause and a conclusion in the then clause.
Given the conditional statements, try interchanging the hypothesis and the conclusion. Give students page to read the definitions of converse, inverse, and contrapositive statements. Write the converse, the inverse, and the contrapositive of the conditional statement. For each exercise below, a write the converse, b determine the truth value of the statement. We explain converse, inverse, and contrapositive of an ifthen statement with video tutorials and quizzes, using our many waystm approach from multiple teachers.
Converse inverse contrapositive worksheets teacher. Converse inverse contrapositive printable worksheets. Here you will examine the implications of the inverse, converse and contrapositive. Use this packet to help you better understand conditional statements. This will include a identifying the converse, inverse, and contrapositive of a conditional statement. Find the converse, inverse, and contrapositive of conditional. Create additional stanzas using related if, then statements. In classical logic, an implication is logically equivalent to its contrapositive, and, moreover, its inverse is logically equivalent to its converse.
If get a nice tan, then you when to florida for spring break. Converses, contrapositives and proof by the contrapositive. Worksheets are converse and contrapositive work 3, inverse converse contrapositive and, logic and conditional statements, lesson practice a conditional statements, geometry notes inductive reasoning conditional, unit 4 logic packet, geometry work using logical reasoning, geometry. Some of the worksheets displayed are converse and contrapositive work 3, inverse converse contrapositive and, logic and conditional statements, lesson practice a conditional statements, geometry notes inductive reasoning conditional, unit 4 logic packet, geometry work using logical. A conditional statement is logically equivalent to its contrapositive. Converse, inverse, and contrapositive statements this activity.
For each statement below, write a the converse, b the inverse, and c the contrapositive. They complete the chart and color boxes with true statements in order to notice that the truth values of the original conditional statement and its contrapositive. Ixl converses, inverses, and contrapositives geometry. Again in symbols, the contrapositive of p q is the statement not q not p, or q p. Converse inverse contrapositive teacher worksheets. If necessary, rewrite the conditional statement in ifthen form. Geometry lesson 10 v2 converse, inverse, contra positive and biconditional free download as pdf file. Write in words a the inverse, b the converse, and c the contrapositive of that conditional.
Secondary i conditional statements worksheet name write the. First, change the statement into an ifthen statement. Conditional, contrapositive, inverse, converse, and. If the figure is a parallelogram, then the figure is a quadrilateral. Write a conditional statement on the board and under it, write the converse, inverse, and. If an animal is black and white, then it is a penguin. Statements with the same truth values are logically equivalent. A biconditional statement can be written when a conditional statement and its converse.
Converse, inverse, and contrapositive type of statement words symbols conditional ifthen form p q converse exchange the hypothesis and conclusion q p inverse negating the hypothesis and conclusion p q contrapositive negating the converse of the conditional q p ma. If a dog is not large, then it is not a great dane. Converse, inverse, and contrapositive of an ifthen. You can write the converse, inverse, and contrapositive of a conditional. In this geometry worksheet, students identify the inverse, converse and contrapositive of each sentence. See how the converse, contrapositive, and inverse are obtained from a conditional statement by changing the order of statements and using. Write a inverse, b converse, c contrapositive of the following statement. This packet will cover ifthen statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional.
The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit. Determine if each resulting statement is true or false. I only offer a bit of clarification and some precision. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Worksheet geometry inverses, contrapositives, and indirect reasoning worksheet. If a conditional is true then the contrapositive is true. The logical converse and inverse of the same conditional statement are logically equivalent to each other. For instance, if it rains, then they cancel school.
The contrapositive okay, enough with the warmup, now its time to get really weird. Unit 4 logic packet humble independent school district. If go to florida for spring break, then you will get a nice tan. What are the differences between inverse, converse, and. This lesson will help you with ideas for teaching these statements and their alternate forms. Write the contrapositive and inverse of each statement. Geometry lesson 10 v2 converse, inverse, contra positive and. If you eat all of your vegetables, then you will grow. It is very important to realize that these two implications are not logically equivalent. Write the converse of each statementand decide whether the converse is true or false. Converse, inverse, contrapositive, conditional statements and. Finally, if you negate everything and flip p and q taking the inverse of the converse, if youre fond of wordplay then you get the contrapositive.
Asked in calculus, definitions, geometry what is converse inverse and contrapositive. They explore conditional statements and what makes them true. Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. Showing top 8 worksheets in the category converse inverse contrapositive.
This lesson targets the converse, inverse, contrapositive of a conditional and then introduces biconditionals in the study of logic. Displaying all worksheets related to converse inverse contrapositive. Converse, inverse, and contrapositive ck12 foundation. Inverse, converse, and contrapositive ck12 foundation. If two points are on the same line, then they are collinear. If water is frozen, then its temperature is below 0c. Write a true conditional statement whose inverse is false. The negation of a statement simply involves the insertion of the word not at the proper part of the statement. If jennifer is not alive, then jennifer does not eat food. Types of statements converse, inverse, contrapositive 1. Types of statements converse, inverse, contrapositive. Logical and conditional statements virginia department of. It can be modified to only focus on converse, inverse, contrapositive or just biconditionals.
Learn vocabulary, terms, and more with flashcards, games, and other. A logical statement that has two parts, a hypothesis and a conclusion. Using logical reasoning from prentice hall geometry book, 4. Some of the worksheets displayed are unit 4 logic packet, logic and conditional statements, lesson practice a conditional statements, conditional statements, geometry, geometry, converse and contrapositive work 3. Displaying all worksheets related to conditional converse inverse contrapositive. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Logic and proof converse, inverse, and contrapositive. Jacob wigfields answer is quite right and his example is very helpful. If you do not go to class, then you get a detention. Converse, inverse, and contrapositive find the converse, inverse, and contrapositive. Lewis carroll, the author of alices adventures in wonderland and through.
Define converse, inverse, contrapositive, and biconditional statement. Write the converse, inverse, and contrapositive of the conditional statement. Students must also identify truth values and give counterexamples for false statements. The inverse, converse and contrapositive are each related to the. Moveable gray and white boxes reveal key information.
Given an ifthen statement if p, then q, we can create three related statements. This lesson will present how to determine if a newly written statement is the converse, inverse, or contrapositive of an ifthen statement. Showing top 8 worksheets in the category conditional converse inverse contrapositive. However, the contrapositive of a true conditional is always true, and the contrapositive of a false conditional is always false. The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional.
What are the converse, contrapositive, and inverse. Conditional converse inverse contrapositive worksheets. Conditional statements converse, inverse, contrapositive. If the converse is true, combine it with the original statement to form a true biconditional statement. Contrapositive, inverse, converse, conditional, and biconditional. For any conditional statement there are several other similarsounding conditional statements. The contrapositive of a conditional statement of the form p. Write the converse of each conditional statement below.
Oct 09, 2016 conditional statements converse, inverse, contrapositive. Likewise, the converse and inverse of a conditional are either both true or both false. Jul 18, 2015 this twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. Write the converse, inverse, and contrapositive of each conditional statement and decide if each statement is true of false. Converse, inverse, contrapositive, conditional statements. Use the law of detachment to reach a logical conclusion about the following statement. Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. Example 15 write the inverse, converse, and contrapositive of the conditional statement. Converse, inverse, and contrapositive of an ifthen statement. Lets compare the converse and inverse statements to see if we can make any judgments about them.
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