Question

1.

a) a Write x + y as a sum-of-products in the variables x and y.

b) Write x(y + 1) as a sum-of-products in the variables x and y.

c) Write (x + y)(x + y) as a sum-of-products in the variables x and y.

d) Write 1 as a sum-of-products in the variables x and y.

2. Verify both distributive Laws using Truth Table

Answer 1

Part (a):

X	Y	R
0	0	0
0	1	1
1	0	1
1	1	1

Since we need to take those outputs for which result is 1 we get  the required expression is .

Part-B;

We again do the truth table as done above.

The sum of product form is

Part-C:

We again do the truth table as done above.

Here the output is 1 when (x=0,y=1) and (x=1,y=0).

Thus the required form is .

Part-D: