Conditional statements are also called if/then statements because if an event Q follows from an event P, the conditional statement is if P, then Q. 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 conditional statement relates two events where the second event depends on the first. 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. Let’s start with a conditional statement and turn it into our three other statements. An example will help to make sense of this new terminology and notation. So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”. The positions of (p) and (q) of the original statement are switched, and then the opposite of each is considered: (sim q rightarrow sim p) (if not (q), then not (p)). 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. (e) \(r\Rightarrow p\), which is true regardless of the whether \(r\) is true or false.Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) LaTeX2e in 90 minutes, by Tobias Oetiker, Hubert Partl, Irene Hyna, and Elisabeth Schlegl. (d) \(q\Rightarrow r\), which is true regardless of the whether \(r\) is true or false. LaTeX Math Symbols The following tables are extracted from The Not So Short Introduction to LaTeX2e, aka. (c) \((p\vee q)\Rightarrow r\), which is true if \(r\) is true, and is false if \(r\) is false. (b) \(p\Rightarrow r\), which is true if \(r\) is true, and is false if \(r\) is false. For Niagara Falls to be in New York, it is sufficient that New York City will have more than 40 inches of snow in 2525.
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