Page 94 - ComputerScience_Class_11

Q = “ There is a prediction for a cyclone”
R = “There will be damage to life and property”
Write these statements in symbolic form.
a. If there is a prediction for a cyclone, then it is raining heavily and there will be damage to life and property.
b. It is raining heavily and there is a prediction of a cyclone.
c. There is a prediction for a cyclone if and only if it is raining heavily.
d. It is not raining heavily or there is no prediction for a cyclone.
e. If there is a prediction for a cyclone, then there will be damage to life and property.
3. Consider the following propositions:
P = “It is raining heavily”
Q = “There is a prediction for cyclone”
R = “There will be damage of life and property”
Express the following statements in words.
a. ∼P ∨ ∼Q
b. ∼P ∨ (∼Q ∧ ∼R)
c. ∼P ↔ ∼Q
d. ∼(P ∧ Q ∧ R)
e. ∼Q → ∼R
4. Write the converse, inverse and contrapositive for the following propositions:
a. If you work hard, then you will crack IIT.
b. If the flower has a beautiful smell, then it is a rose.
c. If I am invited to a party, then I will wear my red gown.
d. If India wins World Cup cricket, then we will celebrate.
e. If a number is equal to its reverse, then it is a palindrome.
5. Construct a truth table and check if the following propositions are tautology, contradiction or contingency:
a. (a) → (a ∧ b)
b. b → (∼a → b) ↔ a
c. (a ∧ b) → (∼a ∧ ∼b)
d. [(a → b) → (b → c)] → a
e. (a ∧ 0) → (∼a ∧ b)
f. a ∧ (a → b) → b
g. (a ↔ b) ∧ (∼a ↔ ∼b)
h. (a ∧ b) → (∼a ∧ b) → (∼b ∧ a)
i. ∼(a ∨ b) ∧ (a ∨ b)
j. ∼(a ∧ b ∧ c) ∨ (a ∧ b ∧ c)
6. Complete the truth table given below:
P Q P → Q (P → Q) → P' ∼((P → Q) → ∼P)

7. Write the Boolean expression for the following logic circuit:
a. ?1? b. ?2? c. ?3? d. ?4?

?1?
A
?3?
?4?
B ?2?

C

92 Touchpad Computer Science (Ver. 3.0)-XI