Advertisements
Advertisements
प्रश्न
Which of the following sentence is a statement? In case of a statement, write down the truth value.
a2 − b2 = (a + b) (a − b) for all a, b ∈ R.
विकल्प
Is a statement
Is not a statement
Advertisements
उत्तर
It is a statement which is true. Hence, its truth value is T.
APPEARS IN
संबंधित प्रश्न
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Congruent triangles are similar.
Write the truth value of the following.
If 3 × 5 = 8 then 3 + 5 = 15.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(p → q) ∧ ∼ r
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that 3x + 8 > 40
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.
Write the truth value of the following statement:
In ΔABC if all sides are equal then its all angles are equal.
Which of the following is not a statement?
Which of the following statements is false?
Choose the correct alternative:
Which of the following is always true?
Choose the correct alternative :
If p is the sentence ‘This statement is false’ then
Choose the correct alternative :
Conditional p → q is equivalent to
State whether the following statement is True or False :
Truth value of 2 + 3 < 6 is F.
State whether the following statement is True or False :
Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.
Solve the following :
State which of the following sentences are statements in logic.
Why are you sad?
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Every parallelogram is a rhombus.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
p ↔ (q → ∼ p)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 < 18.
State the truth value of `sqrt(3)` is not an irrational number
State the truth Value of x2 = 25
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number
Write truth values by activity
|
i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square` = `square` ˄ `square` = `square` ii) ~ ( p ˄ r ) = `~(square` ˄ `square)` = `~ square` = `square` iii) p → q = `square → square` = `square` |
If q Λ ∼p is T, then which of the following is correct?
If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.
Consider the following two statements.
Statement p:
The value of sin 120° can be divided by taking θ = 240° in the equation 2 sin `θ/2` = `sqrt(1 + sin θ) - sqrt(1 - sinθ)`.
Statement q:
The angles A, B, C and D of any quadrilateral ABCD satisfy the equation `cos(1/2(A + C)) + cos(1/2(B + D))` = 0
Then the truth values of p and q are respectively.
The position vector of points A and B are `6bar(a) + 2bar(b) and bar(a) -3bar(b)` . If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is 3`bar(a)- bar(b)`.
lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).
