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**MAT 142 Lecture Video Series**

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**More on Conditionals (MAT 142)**

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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.

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Objectives Determine if two statements are equivalent using truth tables. Write an equivalent variation of a given conditional.

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**More on Conditionals (MAT 142)**

Vocabulary converse inverse contrapositive only if biconditional

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**Conditionals Name Symbolic Form Conditional Converse Inverse**

Contrapositive

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**Using the statements below, write the sentence representation of each of the symbolic expressions :**

I am a multimillion-dollar lottery winner. q: I am a world traveler.

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**Using the statements below, write the sentence representation of each of the symbolic expressions :**

I am a multimillion-dollar lottery winner. q: I am a world traveler.

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**Using the statements below, write the sentence representation of each of the symbolic expressions :**

I am a multimillion-dollar lottery winner. q: I am a world traveler.

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**Using the statements below, write the sentence representation of each of the symbolic expressions :**

I am a multimillion-dollar lottery winner. q: I am a world traveler.

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**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.

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**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.

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**Determine the premise and conclusion of the statement:**

I eat raw fish only if I am in a Japanese restaurant. Rewrite the compound statement in standard form.

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**Write the biconditional as a conjunction of two conditionals:**

We eat at Burger World if and only if Ju Ju’s Kitsch-Inn is closed.

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Translate the two statements into symbolic form and use truth tables to determine whether the statements are equivalent. If I do not have health insurance, I cannot have surgery. If I can have surgery, then I do have health insurance.

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**Determine which pairs of statements are equivalent.**

If Proposition III passes, freeways are improved. If Proposition III is defeated, freeways are not improved. If the freeways are not improved, then Proposition III does not pass. If the freeways are improved, Proposition III passes.

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Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University

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Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.4 Equivalent Statements.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.4 Equivalent Statements.

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