Advertisements
Advertisements
प्रश्न
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
उत्तर
Let p : Himalayas are the highest mountains.
q : Himalayas are the part of India in the north east.
The truth values of p and q are T and T respectively.
The given statement in symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ T ≡ T
∴ Truth value of the given statement is T.
APPEARS IN
संबंधित प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
Construct the truth table of the following:
p → (q → p)
Write the negation of the following statement.
2 + 3 ≠ 5
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 → q) ∨ (r ∧ s)
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.
The necessary condition for existence of a tangent to the curve of the function is continuity.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not 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
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Write the negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Negation of p → (p ˅ ∼ q) is ______
Find the negation of 10 + 20 = 30
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
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)