1.8 Statements of LOGIC Conditional Statement Form “If……then…….”

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Presentation transcript:

1.8 Statements of LOGIC Conditional Statement Form “If……then…….”

Declarative sentence. 2 straight <‘s are =. Conditional Form Declarative sentence 2 straight <‘s are = Conditional Form If 2 <‘s are straight <‘s, then they are =.

Negation of p is: “not p” ~p “If………” hypothesis “….,then……” conclusion “If p then q” p q Negation of p is: “not p” ~p It is raining. Negation: It is not raining. p ~p

Negation of not p ~~p = p It is not raining. It is raining. Not(not p) = p p Converse: (If q, then p) reverse Inverse: (If ~p then ~q) negate Contrapositive: (If ~q, then ~p) negate and reverse

Use a Venn Diagram to solve problems. Conditional Statement: If I was born in St. Louis, then I was born in Missouri. Converse: If I was born in MO, then I was born in St. Louis. (false) q p MO. MO. St. L St. L St. L

Inverse: If I wasn’t born in St. Louis, then I wasn’t born in MO Inverse: If I wasn’t born in St. Louis, then I wasn’t born in MO. (false, I could have been born in MO.) ~p ~q Contrapositive: If I wasn’t born in MO, then I wasn’t born in St. Louis. (true) ~q ~p

GET UP AND STRETCH  With a partner, draw a Venn diagram for the following conditional sentence. If Blake is a member of the Akimel A-al soccer team, then he is a student at Akimel A-al. Write the… Converse Inverse Contrapositive State the truth value of the new statements! False False True

Theorem 3: If a conditional statement is true, then the contrapositive of the statement is also true. If p then q If ~q then ~p Symbol read as “implies” Means equivalent to. Statement and contrapositive are logically equivalent.

Chain of reasoning: If p q true If q r true then p r can conclude by transitive property

Write a conclusion from the given statements. Rearrange to solve. a b d ~c ~c a b f Hint: look for variables that appear only once(they start or stop the chain) Those that appear more are transitions.

Rearranged: d ~c ~c a a b b f Conclusion: d f