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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1. Conditional Statements

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Exercise 48 Page 449

Have the hypothesis and conclusion been interchanged? Has anything been negated? (These are leading questions, by the way.)

Statement: Inverse
Conditional statement: p→ q
Inverse: ~ p→ ~ q

Practice makes perfect

Let's first identify the hypothesis, p, and the conclusion, q, of our conditional statement. If I rode my bike to school, then I did not walk to school.

Examining the second if-then statement, we see that the hypothesis and conclusion have not been exchanged. This means it can neither be the converse q→ p, or the contrapositive, ~ q→~ p. What we do notice is that both the hypothesis and conclusion have been negated. If I did not ride my bike to school then I walked to school This fits the description of the inverse. To represent the statements using symbols, we remember that p is the hypothesis and q is the conclusion. Conditional statement:& p → q Inverse:& ~ p → ~ q

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450