Advertisements
Advertisements
Question
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Options
True
False
Advertisements
Solution
False
APPEARS IN
RELATED QUESTIONS
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Evaluate: ∫ x . log x dx
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
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 negation of the following statement.
− 3 is a natural number.
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.
Mona likes Mathematics and Physics.
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.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
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 ∆ABC is not equilateral, then it is not equiangular.
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 negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Negation of p → (p ˅ ∼ q) is ______
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the negation of p → q
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
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 contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
