Conditional Statements

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Presentation transcript:

Conditional Statements 4/21/2017 Conditional Statements

Methods of Reasoning p 136 Inductive reasoning (use specific examples to make a general rule) Deductive reasoning (apply a general rule to specific examples) Copy into notes (somewhere)

Examples My daddy has curly hair, my brother has curly hair, therefore everyone I am related to has curly hair. All even numbers are divisible by 2 28 is even, therefore 28 is divisible by 2 Inductive reasoning (use specific examples to make a general rule Deductive reasoning (Apply a general rule to specific examples) TRY SOME ON YOUR OWN!

See Page 140 Inductive reasoning (use specific examples to make a general rule) Deductive reasoning (apply a general rule to specific examples)

BOOK QUESTION p .141 Dontrell takes detailed notes in history class and math class. His classmate Trang will miss biology class tomorrow to attend a field trip. Trang’s biology teacher asks him if he knows someone who always takes detailed notes. Trang tells his biology teacher that Dontrell takes detailed notes. Trang’s biology teacher suggests that Trang should borrow Dontrell’s notes because he concludes that Dontrell’s notes will be detailed. What conclusion did Trang make? What information supports this conclusion? What type of reasoning did Trang use? Explain your reasoning. What conclusion did the biology teacher make? What information supports this conclusion? What type of reasoning did the biology teacher use? Explain your reasoning.? Will Trang’s conclusion always be true? Will the biology teacher’s conclusion always be true? Explain your reasoning.

Next, p. 143 “Why is this false?”

Conditional Statement A logical statement with 2 parts 2 parts are called the hypothesis & conclusion Will be written in “if-then” form; such as, “If I can dream it, then I can make it happen.”

Conditional Statement p.12 notes Hypothesis is the part after the word “If” Conclusion is the part after the word “then”

Ex: Underline the hypothesis & circle the conclusion. If you are a brunette, then you have brown hair. hypothesis conclusion

Ex: Rewrite the statement in “if-then” form Vertical angles are congruent. If there are 2 vertical angles, then they are congruent. or If 2 angles are vertical, then they are congruent.

Counterexamples Counterexample: A statement that proves that a statement is false. If you are rich, then you will be happy. Counterexample: Many rich people are in therapy or have major problems.

p.148 Discuss

Truth Values Truth Values 4/21/2017

Simple Sentences p: The year is 2001. q: It is September. Compound Sentence : conjunction means ”and” p Λ q : The year is 2001, and it is September. For a conjunction to equal true: All statements must be true. True False q Λ p It is September, and the year is 2001. True True ~p Λ q The year is not 2001 and it is September False True ~p Λ ~q The year is not 2001 and it is not September.

p: The sum of 6 and 3 is 12. q: The difference in 10x and 2x is 8x. Simple Sentences p: The sum of 6 and 3 is 12. q: The difference in 10x and 2x is 8x. Compound Sentence disjunction means “or” p ν q : The sum of 6 and 3 is 12, or the difference in 10x and 2x is 8x. For a disjunction to be true: At least one true statement TRUE FALSE q V p The difference in 10x and 2x is 8x or the sum of 6 and 3 is 12. TRUE TRUE ~p V q The sum of 6 and 3 is not 12 or the difference in 10x and 2x is 8x. True FALSE ~p V ~q The sum of 6 and 3 is not 12 or the difference of 10x and 2x is not 8x.

Try these: Find the Truth Value p: Today is Saturday. q: It is daytime. p q p q ~p q p ~ q ~ (q p) p → ~ q

p= Vertical angles are congruent. q= Straight angles measure 90º . r= This is the month of June. s= Acute Angles are less than 90º . 33 Find the truth value of each conjunction or disjunction.

4/21/2017