If a dog is not large, then it is not a great dane. This packet will cover ifthen statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional. Write a inverse, b converse, c contrapositive of the following statement. Write the converse, inverse, and contrapositive for each of the following conditional statements. Converses, contrapositives and proof by the contrapositive. I only offer a bit of clarification and some precision. This video gives more detail about the mathematical principles presented in converse inverse contrapositive. Were going to look at these three terms using this statement, if something is a dog, then it is a mammal. This twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. If two segments are congruent, then they have the same length. Converse, inverse, and contrapositive statements this activity should be done after you have discussed conditional statements.
Write the converse of each conditional statement below. If you are a musician, then you are a guitar player. For any conditional statement there are several other similarsounding conditional statements. The negation of a statement simply involves the insertion of the word not at the proper part of the statement. Students must also identify truth values and give counterexamples for false statements. Negations of quantified statements the negation of a universal statement all are is logically equivalent to an existential statement some are not or there is at least one that is not. Learn vocabulary, terms, and more with flashcards, games, and other. Determine if the relationship is proportional worksheet. It is not possible to determine whether or not the converse and inverse of a statement are true if all you have is knowledge of the original statement, although if either the converse or inverse of a statement is true, the other is true as well.
Make a conclusion about the relative truth of the converse and inverse of a conditional statement. The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit. Inverse, converse and contrapositive worksheet for 9th 11th. Moveable gray and white boxes reveal key information. 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. Converse, inverse, contrapositive homesweet learning. Asked in calculus, definitions, geometry what is converse inverse and contrapositive.
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. It is very important to realize that these two implications are not logically equivalent. These new statements are called the converse, inverse, and contrapositive statements. However, the contrapositive of a true conditional is always true, and the contrapositive of a false conditional is always false. Conditional, contrapositive, inverse, converse, and. Worksheet geometry inverses, contrapositives, and indirect reasoning worksheet. If water is frozen, then its temperature is below 0c.
Now if you take a second to think about that, thats true. Improve your math knowledge with free questions in converses, inverses, and contrapositives and thousands of other math skills. The contrapositive okay, enough with the warmup, now its time to get really weird. Unit 4 logic packet humble independent school district. Oct 09, 2016 conditional statements converse, inverse, contrapositive. Conditional converse inverse contrapositive worksheets. The inverse and converse in logic are two ways of rewriting a statement with predefined structures. Displaying all worksheets related to conditional converse inverse contrapositive. Again in symbols, the contrapositive of p q is the statement not q not p, or q p. Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. Converses, contrapositives and proof by the contrapositive the converse of the implication p q is the reverse implication q p. By having students choose their own statements, they cant determine. Conditional statements converse, inverse, contrapositive. This lesson targets the converse, inverse, contrapositive of a conditional and then introduces biconditionals in the study of logic.
Logic and proof converse, inverse, and contrapositive. Find the converse, inverse, and contrapositive of conditional statements. Converse, inverse, and contrapositive on exercise topics. Write the contrapositive and inverse of each statement. This lesson will help you with ideas for teaching these statements and their alternate forms.
Whenever a conditional statement is true, its contrapositive is also true and vice versa. Based on the picture alone, determine if each statement is true or false. Aug 11, 2014 here youll learn how to find the converse, inverse and contrapositive of a conditional statement. Write a true conditional statement whose inverse is false. Sophie alpert on converse, inverse, and contrapositive. Create additional stanzas using related if, then statements. Converse, inverse, and contrapositive find the converse, inverse, and contrapositive. What are the differences between inverse, converse, and.
Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. Determine if each resulting statement is true or false. 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. Conditional and biconditional statements worksheets. Write the converse, inverse, and contrapositive of each conditional statement and decide if each statement is true of false. Converse inverse contrapositive worksheets teacher. 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 9th 11th grade. Converse inverse contrapositive worksheets printable. Distributive property of multiplication worksheet ii. Converse inverse contrapositive printable worksheets. Jacob wigfields answer is quite right and his example is very helpful.
Inverse, converse and contrapositive worksheet for 9th. Converse, inverse, and contrapositive statements read. Use this packet to help you better understand conditional statements. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. You will also learn how to determine whether or not a statement is biconditional. First, change the statement into an ifthen statement. Contrapositive, inverse, converse, conditional, and biconditional. Write a conditional statement on the board and under it, write the converse, inverse, and. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
If an animal is black and white, then it is a penguin. Write the converse, inverse, and contrapositive for each of the following conditional. 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 always match. Nature of the roots of a quadratic equation worksheets. Showing top 8 worksheets in the category converse inverse contrapositive. It can be modified to only focus on converse, inverse, contrapositive or just biconditionals. Worksheets are unit 4 logic packet, logic and conditional statements, lesson practice a conditional statements, conditional statements, geometry, geometry, converse and contrapositive work 3. Conditional, converse, inverse, and contrapositive homework find the inverse, converse, and contrapositive of the statement. Converse inverse contrapositive teacher worksheets. Converse, inverse, and contrapositive learning targets. For instance, if it rains, then they cancel school.
If two points are on the same line, then they are collinear. With aspects of the implication in our rear view mirror, we now want to form new compound statements from that original implication. Identify the converse, inverse, contrapostive of the given conditional statement. Similarly, a statements converse and its inverse are always either both true or both false. What are the converse, contrapositive, and inverse.
Write in words a the inverse, b the converse, and c the contrapositive of that conditional. Displaying all worksheets related to converse inverse contrapositive. In this geometry worksheet, students identify the inverse, converse and contrapositive of each sentence. Likewise, the converse and inverse of a conditional are either both true or both false. Give students page to read the definitions of converse, inverse, and contrapositive statements. I think students will quickly realize not to do that whether we tell them or not and it seems to make adding detailed sentencespecific hints a bit more awkward. Inverse converse contrapositive biconditional truth value negation counterexample conjecture.
Conditional and biconditional statements worksheets solution. 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. Converse, inverse, and contrapositive examples video. Name the relationship between the answer to exercise 7 and ifp, then q. The converse of an inverse is the contrapositive, which is logically equivalent to the original conditional. Ixl converses, inverses, and contrapositives geometry. Use the law of detachment to reach a logical conclusion about the following statement. The logical converse and inverse of the same conditional statement are logically equivalent to each other. If it rains today, soccer practice will be canceled. Interactive word wall, thinkpairshare, group presentation, discussion groups. If the converse is true, then the inverse is true, and vice versa. Given a conditional statement if p, then q if it rains, then they cancel school. A conditional statement consists of two parts, a hypothesis in the if clause and a conclusion in the then clause.
Showing top 8 worksheets in the category conditional converse inverse contrapositive. Converse, inverse, and contrapositive the math doctors. In classical logic, an implication is logically equivalent to its contrapositive, and, moreover, its inverse is logically equivalent to its converse. Students will be asked to identify the converse or inverse or contrapositive of a given conditional statement. Vocabulary organizer, suggested learning strategies. Rewrite the following conditional statements in ifthen form. Variations on the conditional statement direct statement converse inverse contrapositive if p, then q. You may need to rewrite the statement in ifthen form first. Write the converse, the inverse, and the contrapositive of the conditional statement. Write the contrapositive of the converse of if p, then q. If you are a guitar player, then you are a musician. Statements with the same truth values are logically equivalent. To form the converse of the conditional statement, switch the hypothesis and the conclusion.
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