# Deductive vs Inductive Reasoning

More on Conditionals Objectives Write the converse, inverse, and contrapositive of a given conditional statement. Determine the premise and conclusion of a given conditional statement. Rewrite a given conditional statement in standard if . . ., then . . . form. Rewrite a biconditional as the

conjunction of two conditionals. Objectives Determine if two statements are equivalent using truth tables. Write an equivalent variation of a given conditional. Vocabulary converse inverse

contrapositive only if biconditional Conditionals Name Symbolic Form Conditional p q Converse q p

Inverse ~ p ~q ~q ~ p Contrapositiv e Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar

lottery winner. q: I am a world traveler. p q Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner.

q: I am a world traveler. q p Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler.

~ p ~q Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler. ~q ~ p

Write the converse, inverse, and contrapositive of the sentence: If you do not eat meat, you are a vegetarian Converse If you are a vegetarian, : then you do not eat meat. Inverse: If you do eat meat, then

you are not a vegetarian. Contrapositive : If you are not a vegetarian, then you do eat meat. Write the converse, inverse, and contrapositive of the sentence:

You do not win, if you do not buy a lottery ticket. Converse If you do not win, then you : do not buy a lottery ticket. Inverse: If you buy a lottery ticket, then you win. Contrapositive

: If you win, then you buy a lottery ticket. Determine the premise and conclusion of the statement: premise conclusion

I eat raw fish only if I am in a Japanese restaurant. Rewrite the compound statement in standard form. Write the biconditional as a conjunction of two conditionals: We eat at Burger World if an only if Ju

Jus Kitsch-Inn is closed. Translate the two statements into symbolic form and use truth tables to determine whether the statements are equivalent. 1.If I do not have health insurance, I cannot have surgery. 2.If I can have surgery, then I do have

health insurance. Determine which pairs of statements are equivalent. 1.If Proposition III passes, freeways are improved. 2.If Proposition III is defeated, freeways are not improved. 3.If the freeways are not improved, then Proposition III does not pass. 4.If the freeways are improved,

Proposition III passes.

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