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State and verify the associative law using the Truth table.
Answer:
Associative law states that:
- (A+B)+C = A+(B+C)
- (A.B).C = A .(B.C)
Proving using truth table:
|
A |
B |
C |
(A+B) |
(A+B)+C |
(B+C) |
A+(B+C) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
1 |
1 |
1 |
|
0 |
1 |
0 |
1 |
1 |
1 |
1 |
|
0 |
1 |
1 |
1 |
1 |
1 |
1 |
|
1 |
0 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
1 |
1 |
1 |
1 |
1 |
|
1 |
1 |
0 |
1 |
1 |
1 |
1 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
Hence, from the truth table, we have proved that (A+B)+C = A+(B+C) .
|
A |
B |
C |
(A.B) |
(A.B).C |
(B.C) |
A.(B.C) |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
|
0 |
1 |
1 |
0 |
0 |
1 |
0 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
1 |
0 |
1 |
0 |
0 |
0 |
0 |
|
1 |
1 |
0 |
1 |
0 |
0 |
0 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
Hence, from the truth table, we have proved that (A.B).C = A.(B.C) .
