Page 90 - ComputerScience_Class_11

3. Draw a logic circuit diagram to represent AND or and NOT gates using NOR gate only.
Ans. a. NOT gate using NOR gate
A (A+A)' A' (A+A)'

A =A'

b. OR gate using NOR gate

A (A+B)' (A+B)
B

c. AND gate using NOR gate
A
A'
A
A.B (A'+B)')'
= A" . B"
= A . B
B B'
B

4. Prove ∼(a → b) ∨ (∼a ∨ (a ∧ b)) is a tautology.
Ans. a b ∼a a → b ∼(a → b) a ∧ b ∼a ∨ (a ∧ b) ∼(a → b) ∨ (∼a ∨ (a ∧ b))
0 0 1 1 0 0 1 1
0 1 1 1 0 0 1 1
1 0 0 0 1 0 0 1
1 1 0 1 0 1 1 1
The final column results in 1. So, it is a tautology. Hence proved.
5. If, A = “The Taj Mahal is one of the seven wonders of the world” and
B = “It is a favourite tourist destination”
Then, write the statements for the following propositions:
a. A ∧ B b. A → B c. A ↔ B d. A' ∨ B' e. B' → A
Ans. a. The Taj Mahal is one of the seven wonders of the world and it is a favourite tourist destination.
b. If the Taj Mahal is one of the seven wonders of the world, then it is a favourite tourist destination.
c. The Taj Mahal is one of the seven wonders of the world if and only if it is a favourite tourist destination.
d. The Taj Mahal is not one of the seven wonders of the world or it is not a favourite tourist destination.
e. If it is not a favourite tourist destination, then the Taj Mahal is one of the seven wonders of the world.
6. Draw the truth table of (A ⊙ B) ⊕ C.
Ans. A B A ⊙ B C (A ⊙ B) ⊕ C
0 0 1 0 1
0 0 1 1 0
0 1 0 0 0
0 1 0 1 1
1 0 0 0 0
1 0 0 1 1
1 1 1 0 1
1 1 1 1 0

88 Touchpad Computer Science (Ver. 3.0)-XI