![]() Your homework being eaten does not automatically mean you have a goat. This converse statement is not true, as you can conceive of something … or someone … else eating your homework: your dog, your little brother. Take the first conditional statement from above:Ĭonclusion: … then my homework will be eaten.Ĭonverse: If my homework is eaten, then I have a pet goat. You may "clean up" the two parts for grammar without affecting the logic. ![]() To create a converse statement for a given conditional statement, switch the hypothesis and the conclusion. Whether the conditional statement is true or false does not matter (well, it will eventually), so long as the second part (the conclusion) relates to, and is dependent on, the first part (the hypothesis). If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square.Įach of these conditional statements has a hypothesis ("If …") and a conclusion (" …, then …"). If I ask more questions in class, then I will understand the mathematics better. If I eat lunch, then my mood will improve. If the polygon has only four sides, then the polygon is a quadrilateral. If I have a triangle, then my polygon has only three sides. If I have a pet goat, then my homework will be eaten. In logic, concepts can be conditional, using an if-then statement: Then we will see how these logic tools apply to geometry. To understand biconditional statements, we first need to review conditional and converse statements. One example is a biconditional statement. Geometry and logic cross paths many ways. If we remove the if-then part of a true conditional statement, combine the hypothesis and conclusion, and tuck in a phrase "if and only if," we can create biconditional statements. Both the conditional and converse statements must be true to produce a biconditional statement. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.A biconditional statement combines a conditional statement with its converse statement. Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. Whenever you see “con” that means you switch! It’s like being a con-artist! In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. ![]() ExampleĬontinuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”īiconditional: “Today is Wednesday if and only if yesterday was Tuesday.” In other words the conditional statement and converse are both true. ExampleĬontrapositive: “If yesterday was not Tuesday, then today is not Wednesday” What is a Biconditional Statement?Ī statement written in “if and only if” form combines a reversible statement and its true converse. Inverse: “If today is not Wednesday, then yesterday was not Tuesday.” What is a Contrapositive?Īnd the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both. So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”. Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement. So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.Ĭonverse: “If yesterday was Tuesday, then today is Wednesday.” What is the Inverse of a Statement? Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.” ExampleĬonditional Statement: “If today is Wednesday, then yesterday was Tuesday.” Well, the converse is when we switch or interchange our hypothesis and conclusion. This is why we form the converse, inverse, and contrapositive of our conditional statements. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.īut to verify statements are correct, we take a deeper look at our if-then statements. Sometimes a picture helps form our hypothesis or conclusion. In fact, conditional statements are nothing more than “If-Then” statements! To better understand deductive reasoning, we must first learn about conditional statements.Ī conditional statement has two parts: hypothesis ( if) and conclusion ( then). Here we go! What are Conditional Statements? In addition, this lesson will prepare you for deductive reasoning and two column proofs later on. We’re going to walk through several examples to ensure you know what you’re doing. Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher)
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