Question

according to the boolean algebra absorption law which of the following is correct i) x+xy=x ii) (x+y)=xy iii) xy+y=x iv) x+y=y​

Answer 1

Explanation:

i) Let's solve for x.

x+xy=x

Step 1: Add -x to both sides.

xy+x+−x=x+−x

xy=0

Step 2: Divide both sides by y.

xy/y=0/y

x=0

ii) Let's solve for x.

x+y=xy

Step 1: Add -xy to both sides.

x+y+−xy=xy+−xy

−xy+x+y=0

Step 2: Add -y to both sides.

−xy+x+y+−y=0+−y

−xy+x=−y

Step 3: Factor out variable x.

x(−y+1)=−y

Step 4: Divide both sides by -y+1.

x(−y+1)/−y+1=−y/−y+1

x=−y/−y+1

iii) Let's solve for x.

xy+y=x

Step 1: Add -x to both sides.

xy+y+−x=x+−x

xy−x+y=0

Step 2: Add -y to both sides.

xy−x+y+−y=0+−y

xy−x=−y

Step 3: Factor out variable x.

x(y−1)=−y

Step 4: Divide both sides by y-1.

x(y−1)/y−1=−y/y−1

x=−y/y−1

iv) Let's solve for x.

x+y=y

Step 1: Add -y to both sides.

x+y+−y=y+−y

x=0