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Question 809634: Give a truth table that shows the Boolean value of each of the following Boolean expressions, for every possible combination of input values. Hint: including columns for intermediate expressions is helpful. I have no idea where to start. Could you please help me understand how to make truth tables of them?
a) not (p and q)
b) (not P) and Q
c) (not P) or (not(q)
d) (P and Q) or R
e) (P or R) and (Q or R)
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
I'll do a), c), and e).
To construct a truth table:
Begin every truth table that has two letters like this
p | q |
-------
T | T |
T | F |
F | T |
F | F |
Begin every truth table that has three letters like this:
p | q | r |
-----------
T | T | T |
T } T | F |
T | F | T |
T | F | F |
F | T | T |
F | T | F |
F | F | T |
F | F | F |
Rule for "not":
1. If "not" precedes T, it becomes F
2. If "not" precedes F, it becomes T
Rule for "or:
"or" is T except when there are F's on both sides of "or". Then it's F.
Rule for "and":
"and" is F except when there is T's on both sides of "and". Then it's T.
a) not (p and q)
p | q | p and q | not(p and q) |
--------------------------------
T | T | T | F |
T | F | F | T |
F | T | F | T |
F | F | F | T |
c) (not P) or (not q)
p | q | (not p) | (not q) | (not P) or (not q) |
------------------------------------------------
T | T | F | F | F |
T | F | F | T | T |
F | T | T | F | T |
F | F | T T | T |
e) (P or R) and (Q or R)
P | Q | R | (P or R) | (Q or R) | (P or R) and (Q or R) |
---------------------------------------------------------
T | T | T | T | T | T |
T } T | F | T | T | T |
T | F | T | T | T | T |
T | F | F | T | F | F |
F | T | T | T | T | T |
F | T | F | F | T | F |
F | F | T | T | T | T |
F | F | F | F | F | F |
Edwin
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