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A cereal company includes a prize in 55% of its cereal boxes. If the company produced 27,000 packages of cereal last week, how many packages contained a prize ? a. 4,909b. 12,150 c. 13,500d. 14,850 4.4 warm-up 9

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5.4 Inverse, Contrapositive, and Indirect Reasoning You will review different forms of reasoning.

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Before we begin, there are some terms you need to remember. Conditional: If A, then B. Inverse: If not A, then not B. Converse: If B, then A. Pardekooper p q q p ~p ~q Contrapositive: If not B, then not A. ~q ~p

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Pardekooper Conditional Statements If-then Statement: one statement depends on the result of a condition. Example: ''If Deanna eats the last cookie, then Leon will buy more.'‘ hypothesis conclusion hypothesis conclusion 1st part, If ____ 2nd part, then ____ If, then You forgot p q

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Pardekooper Converse Statements switch the hypothesis and the conclusion Example: ''If Leon buys some more cookies, then Deanna will eat the last one.'‘ conclusion hypothesis conclusion hypothesis 1st part, If ____ 2nd part, then ____ If, then You forgot q p again

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Pardekooper Negation Statements the denial of a statement If a statement is true, then its negation is false. If a statement is false, then its negation is true.

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If this had not been an actual emergency, then the attention signal you just heard would not have been followed by official information, news, or instruction. Meadows&Pardekooper Negation Statements Example:. this had not been an actual emergency the attention signal you just heard would not have been followed by official information, news, or instruction hypothesis:conclusion: Note: The inverse of p → q is ~p → ~q. ‘~’ means ‘not.’

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the attention signal you just heard would not have been followed by official information, news, or instruction this had not been an actual emergencyconclusion: hypothesis: If the attention signal you just heard would not have been followed by official information, news, or instruction, then this had not been an actual emergency. Note: The contrapositive of p → q is ~ q → ~ p. Contrapositive Statements created by negating the hypothesis and conclusion of the converse of the given conditional.

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Here comes the assignment

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Assignment Workbook Page 345 all

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