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
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
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.
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.
Kavita is brilliant and brave.
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.
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 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.
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.
Ramesh is intelligent and he is hard working.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
Let p, q and r be any three logical statements. Which of the following is true?
Converse of the statement q `rightarrow` p 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)
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
