3. Boolean Algebra

Question 1

Precedence Law

Answer 1

AB = A.B
A.B + C = (A.B) + C
A + B.C = A + (B.C)

Question 2

DeMorgan’s Theorem

Answer 2

'Break the line, change the sign'
\_\_\_\_   \_\_  \_\_
(A.B)  = A + B  //Nand Gate
\_\_\_\_   
(A+B) = A̅ . B̅    //Nor Gate
\_\_\_\_
(A̅ . B̅) = A + B
\_\_\_\_ 
(A̅ + B̅) = A . B

Question 3

Distributive Law

Answer 3

A.(B+C) = (A.B) + (A.C)
A+(B.C) = (A+B).(A+C)

Question 4

Associative Law

Answer 4

(A.B).C = A.(B.C) = A.B.C
(A+B)+C = A+(B+C) = A+B+C

Question 5

Commutative Law

Answer 5

A.B = B.A
A+B = B+A

Question 6

A.1

Answer 6

= A

Question 7

A.0

Answer 7

= 0

Question 8

A+1

Answer 8

= 1

Question 9

A+0

Answer 9

= A

Question 10

Absorption Law

Answer 10

X + X . Y = X
Proof:
X + X . Y
= X . 1 + X . Y  //X is equal to X . 1
= X . (Y + 1)  //Distributive Law
= X . 1  //Y or 1 is equal to 1
= X