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प्रश्न
Which of the following statement is true
पर्याय
3 + 7 = 4 or 3 – 7 = 4
If Pune is in Maharashtra, then Hyderabad is in Kerala
It is false that 12 is not divisible by 3
The square of any odd integer is even
उत्तर
It is false that 12 is not divisible by 3
संबंधित प्रश्न
Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n2 + n is an even number and n2 - n is an odd number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
5 + 4 = 13
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x – 3 = 14
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Close the door.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Zero is a complex number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Please get me breakfast.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 = x
State which of the following is the statement. Justify. In case of a statement, state its truth value.
The sum of cube roots of unity is zero.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
Write the truth values of the following.
4 is odd or 1 is prime.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
Write the truth values of the following.
24 is a composite number or 17 is a prime number.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(∼ r ↔ p) → ∼ q
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)] ∨ [(q ∧ r) ∨ (p ∧ r)]
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] ∨ [(q → p) → (∼ s ∨ r)]
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x – 8 = 1
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x is an even number.
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, 2x + 9 > 14
If A = {1, 2, 3, 4, 5} then which of the following is not true?
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
4! = 24.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
π is an irrational number.
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:
∃ n ∈ N such that n + 5 > 10.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
A triangle has ‘n’ sides.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The sum of interior angles of a triangle is 180°
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Please grant me a loan.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Did you eat lunch yet?
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Have a cup of cappuccino.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 ! = 0
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number 2 is the only even prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number of arrangements of 7 girls in a row for a photograph is 7!.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Give me a compass box.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Bring the motor car here.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
It may rain today.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Can you speak in English?
Which of the following is not a statement?
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
The negation of the proposition “If 2 is prime, then 3 is odd”, is ______
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
Fill in the blanks :
Truth value of if x = 2, then x2 = − 4 is –––––––––.
State whether the following statement is True or False :
There are 24 months in year is a statement.
State whether the following statement is True or False :
Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.
State whether the following statement is True or False :
Truth value of `sqrt(5)` is not an irrational number is T.
Solve the following :
State which of the following sentences are statements in logic.
z is a positive number.
Solve the following :
State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.
Solve the following :
State which of the following sentences are statements in logic.
How beautiful the flower is!
Solve the following :
State which of the following sentences are statements in logic.
The square of any odd number is even.
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.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Please carry out my instruction.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
The Himalayas is the highest mountain range.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
0! = 1
Determine the truth value of the following statement.
4 + 5 = 7 or 9 − 2 = 5
Determine the truth value of the following statement.
x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.
Determine the truth value of the following statement.
It is not true that 2 + 3 = 6 or 12 + 3 =5
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ q) → ∼ p.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ ∼ q) ∨ (∼ p ∧ q)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∃ x ∈ A, such that 3x + 2 > 9
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 x2 = 25
State the truth value of (p ˅ ∼p)
State whether the following statement is True or False:
Truth value of `sqrt(3)` is not an irrational number is F
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
The truth value of negation of “London is in England” is ______
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
If p ↔ q and p → q both are true, then find truth values of the following with the help of activity
p ˄ q
|
p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square` p ˄ q i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square` ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square` |
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` |
Which of the following quantified statement is true?
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.
If q Λ ∼p is T, then which of the following is correct?
If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.
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)`.
