Advertisements
Advertisements
प्रश्न
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
उत्तर
Let p : 7 is prime number.
q : Tajmahal is in Agra.
The given statement in symbolic form is p ∧ q.
Its negation is ~(p ∧ q) ≡ ~p ∨ ~q.
∴ The negation of given statement is '7 is not prime number or Tajmahal is not in Agra.'
APPEARS IN
संबंधित प्रश्न
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
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.
Stock prices are high if and only if stocks are rising.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (q ∧ r)
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
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.
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.
Proof is lengthy and it is not interesting.
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
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)
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.
A biconditional statement is the conjunction of two ______ statements.
Find the negation of 10 + 20 = 30
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
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
Which of the following is false?
If p and q are true and rands are false statements, then which of the following is true?
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Conditional of p → q is equivalent to p → ∼ q.
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Converse of the statement q `rightarrow` p is ______.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Write the negation of (p `leftrightarrow` q).
