Conditional statements, converses, counterexamples, truth values worksheet this worksheet contains introductory questions on conditional statements and converses. The converse of a conditional statement is formed by exchanging the hypothesis and conclusion. Write the converse of each conditional statement below. Either way, the truth of the converse is generally independent from that of the original statement. For the categorical proposition all s are p, the converse is all p are s. On the first page, they are given diagrams with one piece of information either. 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 conditional is false then the converse is false. May 17, 2017 1 interpret sentences as being conditional statements. If a figure has three sides, then it is not a triangle.
If you run a red light, then you are breaking a traffic law. Conditional statements, converses, counterexamples, truth values. Magnus university at albany, state university of new york preliminary version 0. If a polygon is a quadrilateral, then it is a square. In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. If a number is greater than 3, then the number is greater than 5. Are necessary and sufficient conditions converse relations. A multiple choice quiz relating to conditional statements their various forms.
Counterexamples is a fun, quick way to highlight how to disprove conjectures by finding a counterexample. Unit 4 logic packet humble independent school district. An example of a conditional statement is shown below. When a conditional statement is written in ifthen form, the if part contains the hypothesis and the then part contains the conclusion. When mary graphed f x xx for x and a counterexample for this conjecture.
If terry lives in tampa, then she lives in florida. If a triangle has exactly one obtuse angle, then it is an obtuse triangle. Identify the hypothesis and conclusion of each conditional. If terry lives in florida, then she lives in tampa. R with the property that 1other counterexamples can be obtained via. The phrase, jennifers white birds is not a logical statement because it lacks meaning. Bring the negation as deeply into the statement as possible. Counterexamples is also a great way to practice constructing viable arguments and critiquing the reasoning of others ccss. If both statements are true or if both statements are false then the converse is true. 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. Geometry worksheet on conditional statements teachers pay. Conditionals, converses, and biconditionals practice test 2. The logical converse and inverse of the same conditional statement are logically equivalent to each other. Then write its converse and tell whether the converse is true or false.
This geometry video tutorial explains how to write the converse, inverse, and contrapositive of a conditional statement if p, then q. Well, in converse statements, the hypothesis and the conclusion exchange places. We now focus our e orts on producing stronger counterexamples to the converse of the ivt. Make use of structure, restate each conditional statement in ifthen.
Given an ifthen statement if p, then q, we can create three related statements. Likewise, if the converse statement is false, then the inverse statement must also be false and vice versa. This geometry lesson covers conditional statements, hypothesis, conclusion, counterexamples, biconditionals, converse, inverse and contrapositive. If a figure is a triangle, then all triangles have three sides. When you have an idea or when someone tells you something, test the idea by trying examples. I can determine the truth value of a conditional and its related statements. 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. The leader usually the teacher, though it can be a student makes a false statement that can be proven false with a counterexample. 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. Counterexamples are used to test the logical validity of a claim not its factual accuracy. This worksheet contains introductory questions on conditional statements and converses. Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement.
Converse statements are conditional statements that is a hypothesis that consist of an if and then clause. Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Conditional, contrapositive, inverse, converse, and biconditional. Grieser page 3 write the conditional ifthen form, converse, inverse, and contrapositive forms of the following statements. Contrapositive formed by negating the hypothesis and conclusion of the converse. Try not to think about this particular point too much. Improve your math knowledge with free questions in counterexamples and thousands of other math skills. Brian scott came up with the same example in the comments. R with the property that 1other counterexamples can be obtained via darbouxs theorem. Start studying conditional, converse, inverse, contrapositive. Geometry worksheet on conditional statements teachers. Write both the converse and the contrapositive of the conditional statement below. Counterexamples a counterexample is an example that disproves a universal for all statement.
Give counterexamples for false conditional statements. More conditional sentence quizzes ultimate trivia quiz on first and second conditional sentences. Obtaining counterexamples is a very important part of mathematics, because doing mathematics requires that you develop a critical attitude toward claims. If a triangle has three sides, then all triangles have three sides. When we revisit our example about the sun, the converse statement would read. For instance, if it rains, then they cancel school. True example rewrite the conditional statement in ifthen form.
If the converse statement is true, then the inverse has to also be true, and vice versa. Interactive word wall, thinkpairshare, group presentation, discussion groups. Converse, inverse, and contrapositive learning targets. Conditionals, converses, and biconditionals practice test write this statement as a conditional in ifthen form. If a triangle is an obtuse triangle, then it has exactly one obtuse angle. Logical statements are utterances that can be tested for truth or falsity. This twopage activity guides students to practice writing conditional statements, converses, and biconditionals about animals and triangles. Vocabulary organizer, suggested learning strategies. Some of those structures of formal logic are converse, inverse, contrapositive and counterexample statements.
You can restate such conditional statements in ifthen form. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Conditional statements may not always be written in ifthen form. Conditional, contrapositive, inverse, converse, and. They determine the truth values of statements and provide counterexamples. Characteristics q p if q then p q implies p not always true may have to change wording examples nonexamples examples. If a figure is a triangle, then it has three angles. Either way, the truth of the converse is generally independent from that of. If you live in springfield, then you live in illinois. This packet will cover ifthen statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional. What are the converse, contrapositive, and inverse.
Converse, inverse, contrapositive given an ifthen statement if p, then q, we can create three related statements. On the first page, they are given diagrams with one piece of. Conditional, converse, inverse, contrapositive flashcards. The negation of a statement simply involves the insertion of the word not at the proper part of the statement. Meaning and examples of converse statements science struck. If a function is differentiable, then it is continuous. Use this packet to help you better understand conditional statements. You will find a lesson plan, note pages for interactive notebook, worksheets, a handson activity, a quiz and a writing piece. Geometry name worksheet counterexamples date period. Logic and conditional statements name date use the following conditional statement to answer the problems.
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