Advertisements
Advertisements
प्रश्न
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Advertisements
उत्तर
Let p : x ∈ A ∩ B
q : x ∈ A
r : x ∈ B
The given statement is p → (q ∧ r).
Its negation is ~[p → (q ∧ r)], and
~[p → (q ∧ r)] ≡ p ∧ ~ (q ∧ r) ≡ p ∧ ~ q ∨ ~ r
∴ The negation of given statement is x ∈ A ∩ B and x ∉ A or x ∉ B.
APPEARS IN
संबंधित प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
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 following statement.
16 is an even number and 8 is a perfect square.
Write the negation of the following statement.
− 3 is a natural number.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
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]
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.
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 a holiday and Ram studies on holiday.
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
To be brave is necessary and sufficient condition to climb the Mount Everest.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
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
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 the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Negation of p → (p ˅ ∼ q) is ______
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
