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प्रश्न
If p → q is an implication, then the implication ∼ q → ∼ p is called its
पर्याय
Converse
Contrapositive
Inverse
Alternative
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उत्तर
Contrapositive
संबंधित प्रश्न
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Evaluate: ∫ x . log x dx
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Construct the truth table of the following statement pattern.
(p ∧ ∼q) ↔ (p → q)
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
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.
Mango is a fruit but potato is a vegetable.
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the truth value of the negation of the following statement.
London is in England.
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
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 → q) ↔ ~(p ∨ 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.
~ (p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q ∧ ~ p
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.
Mona likes Mathematics and Physics.
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 necessary condition for existence of a tangent to the curve of the function is continuity.
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.
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.
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 statement.
∀ n ∈ N, n + 3 > 9.
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
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- If a man is not honest, then he is not a judge.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
