Interactive word wall, thinkpairshare, group presentation, discussion groups. Find the truth values for the converse, inverse, and contrapositive of the implica tions stated below. Write a conditional statement on the board and under it, write the converse, inverse, and. While weve seen that its possible for a statement to be true while its converse is false, it turns out that the contrapositive is better behaved. Types of statements converse, inverse, contrapositive. It turns out that even though the converse and inverse are not logically equivalent to the original conditional statement, they are logically equivalent to one another. If the converse is true, then the inverse is true, and vice versa. I only offer a bit of clarification and some precision. 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. However, the contrapositive of a true conditional is always true, and the contrapositive of a false conditional is always false. Explicitly state which truth value goes to each statement. The contrapositive is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. Write the conditional, converse, inverse, and contrapositive. Give students page to read the definitions of converse, inverse, and contrapositive statements.
Name the relationship between the answer to exercise 7 and ifp, then q. Contrapositive proofs work because if the contrapositive is true, due to logical equivalence, the original conditional statement is also true. Oct 09, 2016 conditional statements converse, inverse, contrapositive. A conditional statement can be compared to the logical converse by switching the hypothesis and conclusion. Some of the worksheets for this concept are 8 the pythagorean theorem and its converse, work section 3 2 angles and parallel lines, converse and contrapositive work 3, preparing the ideal educator, unit 4 logic packet, work hinge theorem chapter 5 name refer to each, logic and conditional statements, geometry. If the negation of a statement uses the word not, then disjunction uses the word or. Write the converse, the inverse, and the contrapositive of the conditional statement. What are the converse, contrapositive, and inverse. Jun 18, 2014 in this video playlist i show you how to solve different math problems for algebra, geometry, algebra 2 and precalculus. Moveable gray and white boxes reveal key information. Converse, inverse, and contrapositive statements read.
Inverse, converse and contrapositive worksheet for 8th 10th. Improve your math knowledge with free questions in converses, inverses, and contrapositives and thousands of other math skills. If the figure is a parallelogram, then the figure is a quadrilateral. The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit. Jacob wigfields answer is quite right and his example is very helpful. In this contrapositive and converse statements worksheet, 10th graders solve and complete 14 different problems. Which statement is the converse of it is a car if it is a 300 zx 1 if it is not a 300 zx, then it is not a car 3 if it is a car, then it is a 300 zx 2 if it is not a car, then it is not a 300 zx 4 if it is a car, then it is not a 300 zx 8. Inverse, converse and contrapositive worksheet for 8th. If n is an integer and m is not, then nm is not an integer. Vocabulary organizer, suggested learning strategies. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Consider the statement if an angle is 90 degrees, then the angle is a right angle. Write in words a the inverse, b the converse, and c the contrapositive of that conditional.
Likewise, the converse and inverse of a conditional are either both true or both false. What is the contrapositive of the statement, if i am tall, then i will bump my head. Ixl converses, inverses, and contrapositives geometry. Use this packet to help you better understand conditional statements. A conditional statement consists of two parts, a hypothesis in the if clause and a conclusion in the then clause. This lesson will help you with ideas for teaching these statements and their alternate forms.
Displaying all worksheets related to inverse converse and contrapositive. Types of statements converse, inverse, contrapositive 1. In this geometry worksheet, learners identify the inverse, converse and contrapositive of each sentence. Write the converse of each conditional statement below. Jul 18, 2015 this twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. Conditional converse inverse contrapositive worksheets. Learn converse, inverse, contrapositive with free interactive flashcards. Write the contrapositive of the converse of if p, then q. Conditional statements converse inverse contrapositive truth value counter example you will receive a worksheet as well as fill in the blank notes with the purchase of this resource. Logic and proof converse, inverse, and contrapositive. Converse, inverse, and contrapositive statements this activity should be done after you have discussed conditional statements. 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. If two points are on the same line, then they are collinear.
If an animal is black and white, then it is a penguin. Displaying all worksheets related to converse inverse contrapositive. Conditional statements and their converse worksheets. Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. Converses, contrapositives and proof by the contrapositive. If an angle is divided into 2 congruent angles, then it has been bisected. 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, and contrapositive find the converse, inverse, and contrapositive. Converse, inverse, and contrapositive learning targets. Determine if each resulting statement is true or false. Note that r 1 is an inverse in the sense that r r 1 domr.
Given statements p and q, and the conditional statement p q, state what the following in simplest symbolic form. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. In this video playlist i show you how to solve different math problems for algebra, geometry, algebra 2 and precalculus. Converse inverse contrapositive worksheets teacher.
Write the converse of the conditional statement below. Write a statement that is logically equivalent to the following. Showing top 8 worksheets in the category conditional converse inverse contrapositive. If n is odd and m is even, then either nm is even or. Converse and contrapositive worksheet 3 for each of the following statements give both the converse and the contrapositive. It can be modified to only focus on converse, inverse, contrapositive or just biconditionals. If an angle has a measure of 120, then it is an obtuse angle. Showing top 8 worksheets in the category converse inverse contrapositive. 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 you subtract a whole number from another whole number, the result is also a whole number. The negation of a statement simply involves the insertion of the word not at the proper part of the statement. Students will practice the necessary skills of conditional statements, converse, inverse, contrapositive.
Showing top 8 worksheets in the category conditional statements and their converse. First, change the statement into an ifthen statement. Mathematical logic is a way of expressing concepts in a formal and specific way. The inverse of the contrapositive of the inverse of the converse of the contrapositive of the converse of the contrapositive of p q. For each statement, determine whether the statement, the converse, andor the contrapositive are true. It is very important to realize that these two implications are not logically equivalent. Inverse converse and contrapositive worksheets lesson. Converse, inverse, and contrapositive of an ifthen statement. They explore conditional statements and what makes them true. Whenever a conditional statement is true, its contrapositive is also true and vice versa.
In this geometry worksheet, students identify the inverse, converse and contrapositive of each sentence. Sep 18, 2014 this twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. Similarly, a statements converse and its inverse are always either both true or both false. Jun 05, 2015 types of statements converse, inverse, contrapositive 1. If the polygon is not triangle, then the polygon has no 3 sides. Find the converse, inverse, and contrapositive of conditional statements. Conditional, contrapositive, inverse, converse, and. For instance, if it rains, then they cancel school.
Students must also identify truth values and give counterexamples for false statements. Were going to look at these three terms using this statement, if something is a dog, then it is a mammal. Worksheets are inverse converse contrapositive and, converse and contrapositive work 3, logic and conditional statements, unit 4 logic packet, function inverses date period, unit 6 math 116 logic, geometry work using logical reasoning, geometry notes inductive reasoning conditional. This lesson will present how to determine if a newly written statement is the converse, inverse, or contrapositive of an ifthen statement.
By denition, the reverse of an implication means the same as the original implicationitself. Unit 4 logic packet humble independent school district. If an angle measures less than 90, then it is an acute angle. Choose from 219 different sets of converse, inverse, contrapositive flashcards on quizlet. Note that in constructing the inverse, converse, and contrapositive you are supposed to leave the universal quantifier alone and just change the implication. Converses, contrapositives and proof by the contrapositive the converse of the implication p q is the reverse implication q p. Conditional statements converse, inverse, contrapositive. Write inverse, converse, and contrapositive following. This twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. First, they write the contrapositive and the converse of each statement. This lesson targets the converse, inverse, contrapositive of a conditional and then introduces biconditionals in the study of logic. Write the inverse of if you are 14 years old then you cant drive a car.
If last month was february, then this month is march. Converse, inverse, and contrapositive if a given conditional statement is true, the converse and inverse are not necessarily true. Some of the worksheets displayed are conditional statements, logic and conditional statements, name class date 2 1a practice work conditional, inverse converse contrapositive and, geometry, unit 4 logic packet, conditional statements and valid arguments, chapter. They complete the chart and color boxes with true statements in order to notice that. Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. If the converse is true, write the biconditional statement. 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. This inverse, converse and contrapositive worksheet is suitable for 8th 10th grade. Now if you take a second to think about that, thats true. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement. Converse, inverse, and contrapositive examples video.
Determine the truth value of each conditional stmt. Contrapositive formed by negating the hypothesis and conclusion of the converse. Logic negation, conjunction, disjunction, conditional. If a dog is not large, then it is not a great dane. 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. Make a conclusion about the relative truth of the converse and inverse of a conditional statement. If the polygon is triangle, then the polygon has 3 sides.
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