Advertisements
Advertisements
प्रश्न
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
If Sunday is not holiday then Ram studies on holiday.
Advertisements
उत्तर
Symbolic form of the given statement is
~ p → ~ q
∴ ~ p → ~ q ≡ ~ T → ~ T
≡ F → F
≡ T
Hence, truth value is T.
APPEARS IN
संबंधित प्रश्न
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Find the truth value of the following statement.
Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ↔ ~(p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p → q
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Write the negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)

The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
Conditional of p → q is equivalent to p → ∼ q.
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
