body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1. Conditional Statements

Continue to next subchapter

Exercise 14 Page 446

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

p	q	~ q	p→ ~ q
T	T	F	F
T	F	T	T
F	T	F	T
F	F	T	T

Practice makes perfect

We are asked to make a truth table to the following conditional statement. p → ~ q To do so, let start by recalling the truth table of the conditional statement p→ q.

p	q	p→ q
T	T	T
T	F	F
F	T	T
F	F	T

To create the truth table for p→ ~ q, we first need 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. With this information, we can complete the truth table.

p	q	~ q	p→ ~ q
T	T	F	F
T	F	T	T
F	T	F	T
F	F	T	T

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450