![]() ![]() ![]() This is page 12 of 13 Page list Last Next Comparing Truth Tables Confirms Our Conjectures The Contrapositive These two truth tables are the same so the statements are logically equivalent. Let’s compare the truth tables for the conditional and the contrapositive.Introduction Instruction Examples Practice p q p q T T T T F F F T T F F T p q ~p ~q ~p ~q T T F F T T F F T T F T T F F F F T T T This is page 11 of 13 Page list Last Next Comparing Truth Tables Confirms Our Conjectures The Inverse The Conditional These two truth tables are not the same so the statements are not logically equivalent. Let’s compare the truth tables for the conditional and the inverse.Introduction Instruction Examples Practice p q p q T T T T F F F T T F F T p q q p T T T T F T F T F F F T This is page 10 of 13 Page list Last Next Comparing Truth Tables Confirms Our Conjectures The Converse The Conditional These two truth tables are not the same so the statements are not logically equivalent. Let’s compare the truth tables for the conditional and the converse.T Introduction Instruction Examples Practice p q p q q p (p q) ( q p) (or p q) T T T T T T F F T F F T T F F F F T T T T A biconditional is true when both p q and q p are true. “ If a polygon has three sides then it is a triangle ” and “ If a figure is a triangle then it is a polygon with three sides ” are both true statements. This is page 5 of 13 Page list Last Next The Biconditional A biconditional (p t) is a more concise way to say (p t) (t p).p t : “A polygon has three sides if and only if it is a triangle.” This is page 4 of 13 Page list Last Next The Connectives – the Biconditional Introduction Instruction Examples Practice t : If a figure is a triangle then it is a polygon with three sides. p : If a polygon has three sides then it is a triangle. A biconditional expresses the notion of if and only if.Contrapositive TRUE TRUE Introduction Instruction Examples Practice If the conditional is true then the contrapositive is also true. ” If Marge isn’t in the Philippines, she can’t be in Cebu. ” The Contrapositive ~q ~p “If Marge does not live in the Philippines, then she does not live in Cebu. This is page 9 of 13 Page list Last Next p q is “If Marge lives in Cebu, then she lives in the Philippines. Inverse TRUE FALSE Introduction Instruction Examples Practice Just because the conditional is true does not mean the inverse is true. ” The Inverse ~p ~q “ If Marge does not live in Cebu, then Marge does not live in the Philippines Marge could still live in the Philippines and not be in Cebu. This is page 8 of 13 Page list Last Next p q is “ If Marge lives in Cebu, then she lives in the Philippines. TRUE Converse FALSE Introduction Instruction Examples Practice ![]() ” Just because the conditional is true does not mean the converse is true. ” The Converse q p “ If Marge lives in the Philippines, then she lives in Cebu. Let’s say p represents the statement “Marge lives in Cebu,” and q represents the statement “Marge lives in the Philippines.” This is page 7 of 13 Page list Last Next p q is “If Marge lives in Cebu, then she lives in the Philippines.They are called: Converse: q p Inverse: ~p ~q Contrapositive: ~q ~p This is page 6 of 13 Page list Last Next Not exactly the same thing in Geometry! If.then statements related to conditionals Do they all mean the same thing? Introduction Instruction Examples Practice There are three other if…then statements related to a conditional statement, p q.Introduction Instruction Examples Practice “ If you will not study hard, then you will not get a good score in the exam.” would be written as ~p ~s. p s : If you will study hard, then you will get a good score in the exam. s : You will get a good score in the exam. We use an arrow, , to represent a conditional. This is page 2 of 13 Page list Last Next The Connectives: The Conditional A conditional expresses the notion of if.This is page 1 of 13 Page list Last Next The Symbols: The Connectives - Conditional and Biconditional Introduction Instruction Examples Practice Negation: NOT Conjunction: AND Disjunction: OR Conditional: if…then Biconditional: if and only if NOT ~ AND OR If…then If and only if We are ready to add the conditional and biconditional to our list of connectives.Please go back or choose a topic from above.How can we tell if a conditional statement is true or false? Introduction Instruction Examples Practice The other two connectives that create compound statements in logic, the conditional statement, and the biconditional statement are often involved in arguments and proofs. Logic and Geometry are both about developing good arguments or proofs that something is true or false.Logic The Conditional and Related Statements Resources: HRW Geometry, Lesson 12.3. ![]()
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