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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 42 Page 448

A conditional statement is only false when a true hypothesis produces a false conclusion.

p	~ q	p → ~ q	~(p → ~ q)
T	F	F	T
T	T	T	F
F	F	T	F
F	T	T	F

Practice makes perfect

Let's remind ourselves of the truth table of a conditional statement.

p	q	p→ q
T	T	T
T	F	F
F	T	T
F	F	T

To create our truth table for ~ (p→ ~ q), we first have to negate q. The truth value of a negation is the opposite of the truth value of the original statement.

q	~ q
T	F
F	T
T	F
F	T

Note that a conditional statement is only false when a true hypothesis produces a false conclusion. Also, to get ~(p→ ~ q) means negating the truth value of p→ ~ q. With this, we can create our truth table.

p	~ q	p → ~ q	~( p → ~ q)
T	F	F	T
T	T	T	F
F	F	T	F
F	T	T	F

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450