Advertisements
Advertisements
प्रश्न
Write the negation of the following.
An angle is a right angle if and only if it is of measure 90°.
Advertisements
उत्तर
Let p : An angle is a right angle.
q : An angle is of measure 90°.
The given statement is p ↔ q.
Its negation is ~(p ↔ q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
∴ The negation of the given statement is ‘An angle is a right angle and it is not of measure 90° or an angle is of measure 90° and it is not a right angle.’
APPEARS IN
संबंधित प्रश्न
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Evaluate: ∫ x . log x dx
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.
(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
Write the truth value of the following statement.
16 is an even number and 8 is a perfect square.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
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]
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.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
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.
7 is prime number and Tajmahal is in Agra.
Write the negation of p → q
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Let p: I am brave.
q: I will climb the Mount Everest.
The symbolic form of a statement,
‘I am neither brave nor I will climb the mount Everest’ is
