Question

B : Application Based Questions
In the Boolean Algebra, verify using truth table that X + XY = X for each X, Y in (0,1).​ computer

Answer 1

To solve this question we need to know the following in Boolean algebra:

1) 0 * 0 = 0(AND)

2) 0 * 1 = 0(AND)

3) 1 * 0 = 0(AND)

4) 1 * 1 = 1(AND)

5) 0 + 0 = 0(OR)

6) 0 + 1 = 1(OR)

7) 1 + 0 = 1(OR)

8) 1 + 1 = 1(OR)

Truth Table:

X     Y         XY                  X+XY

0     0       0 * 0 = 0          0 + 0 = 0          X = X + XY

0     1        0 * 1 = 0           0 + 0 = 0          X = X + XY

1     0        1 * 0 = 0           0 + 1 = 1            X = X + XY

1     1         1 * 1 = 1              1 + 1 = 1            X = X + XY

Hence Proved.