Page 71 - computer science (868) class 11
P. 71
R = “There will be damage to life and property”
Write these statements in symbolic form.
i. If there is a prediction for a cyclone, then it is raining heavily and there will be damage to life and property.
ii. It is raining heavily and there is a prediction of a cyclone.
iii. There is a prediction for a cyclone if and only if it is raining heavily.
iv. It is not raining heavily or there is no prediction for a cyclone.
v. 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.
i. ∼P ∨ ∼Q
ii. ∼P ∨ (∼Q ∧ ∼R)
iii. ∼P ↔ ∼Q
iv. ∼(P ∧ Q ∧ R)
v. ∼Q → ∼R
4. Write the converse, inverse and contrapositive for the following propositions:
i. If you work hard, then you will crack IIT.
ii. If the flower has a beautiful smell, then it is a rose.
iii. If I am invited to a party, then I will wear my red gown.
iv. If India wins World Cup cricket, then we will celebrate.
v. 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.
i. (a) → (a ∧ b)
ii. b → (∼a → b) ↔ a
iii. (a ∧ b) → (∼a ∧ ∼b)
iv. [(a → b) → (b → c)] → a
v. (a ∧ 0) → (∼a ∧ b)
vi. a ∧ (a → b) → b
vii. (a ↔ b) ∧ (∼a ↔ ∼b)
viii. (a ∧ b) → (∼a ∧ b) → (∼b ∧ a)
ix. ∼(a ∨ b) ∧ (a ∨ b)
x. ∼(a ∧ b ∧ c) ∨ (a ∧ b ∧ c)
6. Complete the truth table given below:
P Q P → Q (P → Q) → P' ∼((P → Q) → ∼P)
7. Given the following logical circuit:
?1?
A
?3?
?4?
B ?2?
C
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Propositional Logic, Hardware Implementation, Arithmetic Operations 69

