Prentice Hall Geometry

Chapter 2 Reasoning and Proof > Concept Byte: Logic and Truth Tables

A truth table lists all the possible combinations of truth values for two or more statements.

Example	p	q	p rightwards arrow q	p and q	p or q
p: Ohio is a state. q: There are 50 states.	T	T	T	T	T
p: Georgia is a state. q: Miami is a state.	T	F	F	F	T
p : 2 + 2 = 5 p colon , 2 plus , 2 equals , 5 q : 2 · 2 = 4 q colon , 2 middle dot 2 equals , 4	F	T	T	F	T
p: 2 + 1 = 4 2 plus , 1 equals , 4 q: Dolphins are big fish.	F	F	T	F	F

Activity 2

To find the possible truth values of a complex statement such as open s and j close or tilde t comma you can make a truth table like the one below. You start with columns for the single statements and add columns to the right. Each column builds toward the final statement. The table below starts with columns for s, j, and t and builds to open s and j close or tilde t . Copy the table and work with a partner to fill in the blanks.

s	j	t	tilde t	s and j	( s ∧ j ) ∨ ˜ t open s and j close or tilde t
T	T	T	F	T	20. modified question mark with under bar below
T	T	F	13. modified question mark with under bar below	T	T
T	F	T	F	F	21. modified question mark with under bar below
T	F	F	T	17. modified question mark with under bar below	T
F	T	T	14. modified question mark with under bar below	F	22. modified question mark with under bar below
F	T	F	15. modified question mark with under bar below	F	23. modified question mark with under bar below
F	F	T	F	18. modified question mark with under bar below	F
10. modified question mark with under bar below	11. modified question mark with under bar below	12. modified question mark with under bar below	16. modified question mark with under bar below	19. modified question mark with under bar below	24. modified question mark with under bar below

Make a truth table for the statement ( ˜ p ∨ q ) ∧ ˜ r . open tilde p or q close and tilde r .
1. Make a truth table for tilde open p and q close . Make another truth table for tilde p or tilde q .
2. Make a truth table for tilde open p or q close . Make another for tilde p and tilde q .
3. DeMorgan's Law states that ˜ ( p ∧ q ) = ˜ p ∨ ˜ q tilde open p and q close equals tilde p or tilde q and that ˜ ( p ∨ q ) = ˜ p ∧ ˜ q . tilde open p or q close equals tilde p and tilde q . How do the truth tables you made in parts (a) and (b) show that DeMorgan's Law is true?

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