This lesson will help you with ideas for teaching these statements and their alternate forms. Converse, inverse, biconditional and contrapositive. Identify the type of the given conditional statement. Aug 11, 2014 here youll learn how to find the converse, inverse and contrapositive of a conditional statement. Converse, inverse, and contrapositive statements this activity. Presuming the original statement to be true that is you have a cell phone that beeps only if the battery is low, then the contrapositive is always true.
Types of statements converse, inverse, contrapositive. Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. Here youll learn how to find the converse, inverse and contrapositive of a conditional statement. Now if you take a second to think about that, thats true. For instance, if it rains, then they cancel school. Explicitly state which truth value goes to each statement. Write the converse of each conditional statement below. The contrapositive is the converse of the inverse or the inverse of the converse if you like. They complete the chart and color boxes with true statements in order to notice.
If a dog is not large, then it is not a great dane. Jacob wigfields answer is quite right and his example is very helpful. A conditional statement consists of two parts, a hypothesis in the if clause and a conclusion in the then clause. Students must also identify truth values and give counterexamples for false statements. Types of statements converse, inverse, contrapositive 1. How do you write the converse, inverse, and contrapositive. If two points are on the same line, then they are collinear. Converse, inverse, and contrapositive of an ifthen statement. Logic with conditional statements, converse, inverse, contrapositives. Write the converse, inverse and contrapositive for each of the following conditional statements determine if each of the three statements is true or false.
The inverse of the contrapositive of the inverse of the converse of the contrapositive of the converse of the contrapositive of p q. If an object is a computer, then it has a hard drive. If it is not saturday, then school is not closed contrapositive. Sep 03, 20 learn how to find the inverse, the converse and the contrapositive of a statement. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement. Learn converse, inverse, contrapositive with free interactive flashcards. Note that r 1 is an inverse in the sense that r r 1 domr. What are examples of a statements converse, inverse, and. Lewis carroll, the author of alices adventures in wonderland and through.
The content, explanations and including practice problems with solution can be learnt using video audio presentation in own hand writing by the instructor and several examples and will help you to apply the developed skills for finding solution to realworld problems. This twopage worksheet contains practice writing biconditionals as well as inverse, converse, and contrapositive statements. Converse, inverse, and contrapositive learning targets. This lesson explains the concepts, how to write and application of the biconditional, inverse, converse, and contrapositives. I only offer a bit of clarification and some precision.
Ixl converses, inverses, and contrapositives geometry. Learn vocabulary, terms, and more with flashcards, games, and other study tools. In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive. This packet will cover ifthen statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional. Investigating advertising slogans using conditional. If an integer x equals 1 or 0, then x 2 is less than or equal to x. First, change the statement into an ifthen statement. Find the converse, inverse, and contrapositive of conditional statements. Logic with conditional statements, converse, inverse. Converses, contrapositives and proof by the contrapositive. The negation of a statement simply involves the insertion of the word not at the proper part of the statement.
In 1 4, write the inverse of the statement in symbolic form. Again in symbols, the contrapositive of p q is the statement not q not p, or q p. Write a conditional statement on the board and under it, write the converse, inverse, and. Interactive word wall, thinkpairshare, group presentation, discussion groups. Remote work advice from the largest allremote company. If the negation of a statement uses the word not, then disjunction uses the word or. In 5 8, write the converse of the statement in symbolic form. Write the converse, inverse, and contrapositive of the given conditional statement. This lesson will present how to determine if a newly written statement is the converse, inverse, or contrapositive of an ifthen statement. We have to write the converse, inverse and contrapositive of the above statement. Choose from 219 different sets of converse, inverse, contrapositive flashcards on quizlet. Find the truth values for the converse, inverse, and contrapositive of the implica tions stated below.
Fasc form of the sta ement conditional statement converse of the conditional statement inverse of the conditional statement. It is very important to realize that these two implications are not logically equivalent. Unit 4 logic packet humble independent school district. Jun 05, 2015 types of statements converse, inverse, contrapositive 1. If it rains today, soccer practice will be canceled. Given statements p and q, and the conditional statement p q, state what the following in simplest symbolic form. The next way we can test for logical equivalences is to find the logical inverse of the conditional statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional. The inverse, converse and contrapositive are each related to the. We explain converse, inverse, and contrapositive of an ifthen statement with video tutorials and quizzes, using our many waystm approach from multiple teachers. If the figure is a parallelogram, then the figure is a quadrilateral. Contrapositive proofs work because if the contrapositive is true, due to logical equivalence, the original conditional statement is also true. Inverse, converse, and contrapositive ck12 foundation. Write the inverse of each conditional statement below.
What are the converse, contrapositive, and inverse. Converse, inverse, and contrapositive of an ifthen. Converse, inverse, and contrapositive ck12 foundation. This will include a identifying the converse, inverse, and contrapositive of a conditional statement. If x, then y has converse as if y, then x, inverse as if no y then no x, contrapositive as if no x, then no y. 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.
If the converse is true, then the inverse is also logically true. Vocabulary organizer, suggested learning strategies. The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit. If an animal is black and white, then it is a penguin. Were going to look at these three terms using this statement, if something is a dog, then it is a mammal. Can somebody explain converse, inverse, contrapositive. If you dont need to charge the battery then the phone isnt. Conditional statementimplication converse and contrapositive. Statement if a person is 18 years old, then he is a legal adult. Consider the statement if an angle is 90 degrees, then the angle is a right angle. Learn how to find the inverse, the converse and the contrapositive of a statement. Converse, inverse, contrapositive given statements p and q, and the conditional statement p q, state what the following in simplest symbolic form.
You will also learn how to determine whether or not a statement is biconditional. What are the differences between inverse, converse, and. Fallacy of the inverse example ii if youre good, youll be rewarded. Converse if a person is a legal adult, then he is 18 years old. What are the converse,the contrapositive and inverse of that statement. Conditional, contrapositive, inverse, converse, and. Logic and proof converse, inverse, and contrapositive. For every conditional statement you can write three related statements, the converse, the inverse, and the contrapositive. Converses, contrapositives and proof by the contrapositive the converse of the implication p q is the reverse implication q p. Converse, inverse, and contrapositive statements read. Give students page to read the definitions of converse, inverse, and contrapositive statements.
Use this packet to help you better understand conditional statements. The contrapositive of the statement has its antecedent and consequent inverted and flipped. Find the converse, inverse, and contrapositive of conditional. The contrapositive, converse, and inverse of an implication. Converse, inverse, and contrapositive find the converse, inverse, and contrapositive. Converse,the contrapositive and the inverse of these condition. If an object is a battery, then it is rechargeable. Logical and conditional statements virginia department of.
Environmental education resources to commemorate earth days 50th anniversary. Converse, inverse, and contrapositive statements this activity should be done after you have discussed conditional statements. Write the converse, the inverse, and the contrapositive of the conditional statement. In classical logic, an implication is logically equivalent to its contrapositive, and, moreover, its inverse is logically equivalent to its converse. 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.
Determine if each resulting statement is true or false. If school is not closed, then it is not saturday dont worry about the statements being true. Write the converse, inverse, and contrapositive of the given. For 16 17, write the converse, inverse, and contrapositive statements for each conditional statement. 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, 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. Improve your math knowledge with free questions in converses, inverses, and contrapositives and thousands of other math skills. If the statement is true, then the contrapositive is also logically true. The inverse is the negative form of the conditional in which both. Investigating advertising slogans using conditional, inverse. How do you write the converse, inverse, and contrapositive of. The contrapositive of this implication is the formula. If you do all of your homework, then you get to play video games. Converse, inverse, and contrapositive examples video.
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