Advertisements
Advertisements
प्रश्न
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
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
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)
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Write the following compound statement symbolically.
If Δ ABC is right-angled at B, then m∠A + m∠C = 90°
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
Milk is white or grass is green.
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.
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.
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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
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.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If the question paper is not easy then we shall not pass.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
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 price increases, then demand falls.
Write the negation of the following.
An angle is a right angle if and only if it is of measure 90°.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high or stocks are not rising iff stocks are rising.
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Write the following statements in symbolic form
Milk is white if and only if the sky is not blue
Write the negation of p → q
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If p and q are true and rands are false statements, then which of the following is true?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Converse of the statement q `rightarrow` p is ______.
The statement ∼(p ↔ ∼q) is ______.
If p, q are true statements and r, s are false statements, then write the truth value of the compound statement
(p `→` ∼ r) `→` (q ∧ s)
