Advertisements
Advertisements
Question
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Options
p ˄ q ˄ ∼ r
(p ˄ q) ˅ r
p ˅ q ˅ ∼ r
(p v q) ˄ (r ˅ s)
Advertisements
Solution
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is p ˄ q ˄ ∼ r.
APPEARS IN
RELATED QUESTIONS
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
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)
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
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.
All men are animals.
Write the negation of the following statement.
− 3 is a natural number.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
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.
It is not true that 3 − 7i is a real number.
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 : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
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.
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 → r
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.
Kanchanganga is in India and Everest is in Nepal.
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.
I will have tea or coffee.
Negation of p → (p ˅ ∼ q) is ______
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Negation of “Some men are animal” is ______.
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
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 q: There are clouds in the sky then p: it is raining. The symbolic form is ______
Which of the following is false?
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Conditional of p → q is equivalent to p → ∼ q.
Let p, q and r be any three logical statements. Which of the following is true?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
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.
