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.

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Presentation transcript:

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, warm-up 9

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

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

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

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

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.

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.’

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.

Here comes the assignment

Assignment Workbook Page 345 all