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
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the negation of the following statement.
2 + 3 ≠ 5
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.
Find the truth value of the following statement.
3 is a prime number and an odd number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ∨ (r ∧ s)
If p and q are true and r and s are false, find the truth value of the following compound statement.
[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]
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.
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.
Kavita is brilliant and brave.
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) ∧ r
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
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.
A biconditional statement is the conjunction of two ______ statements.
Negation of “Some men are animal” is ______.
Which of the following is logically equivalent to `∼(∼p \implies 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 ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
