If a conditional is false then the converse is false. If a function is differentiable, then it is continuous. Bring the negation as deeply into the statement as possible. When we revisit our example about the sun, the converse statement would read. Give counterexamples for false conditional statements. For instance, if it rains, then they cancel school.
Counterexamples is also a great way to practice constructing viable arguments and critiquing the reasoning of others ccss. If the converse statement is true, then the inverse has to also be true, and vice versa. You can play counterexamples as an opening game, but the language of conjectures and counterexamples has the power to animate much deeper rich tasks in the classroom. If a triangle is an obtuse triangle, then it has exactly one obtuse angle. Converse statements are conditional statements that is a hypothesis that consist of an if and then clause. More conditional sentence quizzes ultimate trivia quiz on first and second conditional sentences. Identify the hypothesis and conclusion of each conditional. Improve your math knowledge with free questions in counterexamples and thousands of other math skills. Then write its converse and tell whether the converse is true or false. Conditional statements, converses, counterexamples, truth values worksheet this worksheet contains introductory questions on conditional statements and converses. Logic and conditional statements name date use the following conditional statement to answer the problems.
Brian scott came up with the same example in the comments. If a polygon is a square, then it is a quadrilateral. In inverse statements, the opposite of the original hypothesis and conclusion is written, whereas in a converse statement, only the hypothesis and the conclusion is exchanged. Conditionals, converses, and biconditionals practice test write this statement as a conditional in ifthen form. Use this packet to help you better understand conditional statements. Logical statements are utterances that can be tested for truth or falsity. Magnus university at albany, state university of new york preliminary version 0. Interactive word wall, thinkpairshare, group presentation, discussion groups. Likewise, if the converse statement is false, then the inverse statement must also be false and vice versa.
This buzzle article explains how to write one, along with some examples of converse statements. Contrapositive formed by negating the hypothesis and conclusion of the converse. Either way, the truth of the converse is generally independent from that of. If you live in springfield, then you live in illinois. Conditional statements, converses, counterexamples, truth values. Given an ifthen statement if p, then q, we can create three related statements. For the categorical proposition all s are p, the converse is all p are s. Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. May 17, 2017 1 interpret sentences as being conditional statements. Conditional, contrapositive, inverse, converse, and. When a conditional statement is written in ifthen form, the if part contains the hypothesis and the then part contains the conclusion. The negation of a statement simply involves the insertion of the word not at the proper part of the statement.
Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. When you have an idea or when someone tells you something, test the idea by trying examples. Vocabulary organizer, suggested learning strategies. Conditional statements, converses, counterexamples, truth. The phrase, jennifers white birds is not a logical statement because it lacks meaning. This geometry video tutorial explains how to write the converse, inverse, and contrapositive of a conditional statement if p, then q. If a polygon is a quadrilateral, then it is a square. R with the property that 1other counterexamples can be obtained via. R with the property that 1other counterexamples can be obtained via darbouxs theorem. Counterexamples a counterexample is an example that disproves a universal for all statement. This packet will cover ifthen statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional. Meaning and examples of converse statements science struck.
On the first page, they are given diagrams with one piece of. When mary graphed f x xx for x and a counterexample for this conjecture. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement. This geometry lesson covers conditional statements, hypothesis, conclusion, counterexamples, biconditionals, converse, inverse and contrapositive. If a number is greater than 3, then the number is greater than 5. If a figure is a triangle, then it has three angles. Start studying conditional, converse, inverse, contrapositive.
If terry lives in tampa, then she lives in florida. If a figure is a triangle, then all triangles have three sides. Conditionals, converses, and biconditionals practice test 2. Write the converse of each conditional statement below.
Counterexamples is a fun, quick way to highlight how to disprove conjectures by finding a counterexample. Make use of structure, restate each conditional statement in ifthen. Write both the converse and the contrapositive of the conditional statement below. Converse, inverse, and contrapositive learning targets. The converse of a conditional statement is formed by exchanging the hypothesis and conclusion. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Counterexamples are used to test the logical validity of a claim not its factual accuracy. The logical converse and inverse of the same conditional statement are logically equivalent to each other. True example rewrite the conditional statement in ifthen form. If a triangle has three sides, then all triangles have three sides. The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance. Determine the truth value of the conditional statement, its converse, and its inverse. If a figure has three sides, then it is not a triangle.
This twopage activity guides students to practice writing conditional statements, converses, and biconditionals about animals and triangles. Either way, the truth of the converse is generally independent from that of the original statement. Geometry worksheet on conditional statements teachers. We now focus our e orts on producing stronger counterexamples to the converse of the ivt. On the first page, they are given diagrams with one piece of information either. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. The leader usually the teacher, though it can be a student makes a false statement that can be proven false with a counterexample. If terry lives in florida, then she lives in tampa. Geometry name worksheet counterexamples date period. In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. What are the converse, contrapositive, and inverse. They determine the truth values of statements and provide counterexamples. The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of. A multiple choice quiz relating to conditional statements their various forms.
I can determine the truth value of a conditional and its related statements. Geometry worksheet on conditional statements teachers pay. Characteristics q p if q then p q implies p not always true may have to change wording examples nonexamples examples. Obtaining counterexamples is a very important part of mathematics, because doing mathematics requires that you develop a critical attitude toward claims. A conditional and its converse do not mean the same thing if we negate both the hypothesis and the conclusion we get a inverse statemen t. If a triangle has exactly one obtuse angle, then it is an obtuse triangle. If one counterexample can be found, then the claim is not always true and is not logically valid. You will find a lesson plan, note pages for interactive notebook, worksheets, a handson activity, a quiz and a writing piece. Conditional, contrapositive, inverse, converse, and biconditional. This worksheet contains introductory questions on conditional statements and converses.
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