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Draw the truth table of the following expression:
(A and B) or (not A and not B)
Answer:
Answer by student
The truth table of the expression is:
|
A |
B |
not A |
not B |
A and B |
not A and not B |
(A and B) or (not A and not B) |
|
0 |
0 |
1 |
1 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
0 |
0 |
|
1 |
0 |
0 |
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
0 |
1 |
0 |
1 |
Detailed answer by teachoo:
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To draw the truth table for the given expression (A and B) or (not A and not B), we need to consider all possible combinations of values for variables A and B and evaluate the expression for each combination.
- For the first row (A = 0, B = 0):
- (A and B) evaluates to 0 (0 and 0 = 0).
- (not A and not B) evaluates to 1 (not 0 and not 0 = 1).
- The expression (A and B) or (not A and not B) evaluates to 1 (0 or 1 = 1).
- For the second row (A = 0, B = 1):
- (A and B) evaluates to 0 (0 and 1 = 0).
- (not A and not B) evaluates to 0 (not 0 and not 1 = 0).
- The expression (A and B) or (not A and not B) evaluates to 0 (0 or 0 = 0).
- For the third row (A = 1, B = 0):
- (A and B) evaluates to 0 (1 and 0 = 0).
- (not A and not B) evaluates to 0 (not 1 and not 0 = 0).
- The expression (A and B) or (not A and not B) evaluates to 0 (0 or 0 = 0).
- For the fourth row (A = 1, B = 1):
- (A and B) evaluates to 1 (1 and 1 = 1).
- (not A and not B) evaluates to 0 (not 1 and not 1 = 0).
- The expression (A and B) or (not A and not B) evaluates to 1 (1 or 0 = 1).
So, the truth table of the expression is:
|
A |
B |
not A |
not B |
A and B |
not A and not B |
(A and B) or (not A and not B) |
|
0 |
0 |
1 |
1 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
0 |
0 |
0 |
|
1 |
0 |
0 |
1 |
0 |
0 |
0 |
|
1 |
1 |
0 |
0 |
1 |
0 |
1 |
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