Advertisements
Advertisements
प्रश्न
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Advertisements
उत्तर
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
≡ ~ [T ∨ (F ∧ F)] ∧ ~ [(F ∧ ~ F) ∧ T]
≡ ~ (T ∨ F) ∧ ~ [(F ∧ T) ∧ T]
≡ ~ T ∧ ~ (F ∧ T)
≡ F ∧ ~ F
≡ F ∧ T
≡ F
Hence, truth value is F.
APPEARS IN
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
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)
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.
Sunday is not holiday or Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
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.
Kavita is brilliant and brave.
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.
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
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.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the negation of p → q
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
Conditional of p → q is equivalent to p → ∼ q.
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
Let p: I am brave.
q: I will climb the Mount Everest.
The symbolic form of a statement,
‘I am neither brave nor I will climb the mount Everest’ is
