![]() ![]() 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. 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.” Example Our conditional statement is: if a population consists of 50 men then 50 of the population must be women. A truth table is a mathematical table used in logic specifically in connection with Boolean algebra, boolean functions, and propositional calculus which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. 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.” In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and. Biconditional: Today is Wednesday if and only if yesterday was Tuesday. for alogic NAND gate is denoted by a single dot or full stop symbol, (. ExampleĬonditional Statement: “If today is Wednesday, then yesterday was Tuesday.” Continuing with our initial condition, If today is Wednesday, then yesterday was Tuesday. Section 5.4: The Conditional and Related StatementsEquivalent Forms of the. 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. Example 1.2: Consider the two statements, P: 5 is a prime number, Q: 7 is an even number. Thus, if statement latexP/latex is true then the truth value of its negation is false. In other words, negation simply reverses the truth value of a given statement. P Q P Q T T T T F T F T T F F F Notice that P or Q is true if at least one of the statements is true. Remember: The negation operator denoted by the symbol or latexneg/latex takes the truth value of the original statement then output the exact opposite of its truth value. Sometimes a picture helps form our hypothesis or conclusion. Denition 1.3: The statement P or Q, called the disjunction and denoted by P Q, is dened by the truth table table below. 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. ![]() Niagara Falls is in New York or New York City is the state capital of New York implies that New York City will have more than 40 inches of snow in 2525.Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher).Niagara Falls is in New York only if New York City will have more than 40 inches of snow in 2525.If Niagara Falls is in New York, then New York City is the state capital of New York.What is their truth value if \(r\) is true? What if \(r\) is false? ![]() Represent each of the following statements by a formula. The statement \(p\) is true, and the statement \(q\) is false. New York City will have more than 40 inches of snow in 2525. New York City is the state capital of New York. \)Ĭonsider the following statements: \(p\): ![]()
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