Advertisements
Advertisements
प्रश्न
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
π is an irrational number.
उत्तर
It is a statement which is true, hence its truth value is ‘T’.
APPEARS IN
संबंधित प्रश्न
If p ˄ q = F, p → q = F, then the truth value of p and q is ______.
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.
A quadratic equation cannot have more than two roots.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
All real numbers are whole numbers.
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.
Write the truth values of the following.
64 is a perfect square and 46 is a prime number.
Write the truth values of the following.
It is not true that 5−3i is a real number.
Write the truth value of the following.
Milk is white if and only if sky is blue.
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:
p ∨ (q ∧ 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 ∧ r) ∨ (p ∧ r)]
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 such that 3x + 8 > 40
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
India is a country and Himalayas is a river.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
cos2θ − sin2θ = cos2θ for all θ∈R.
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.
Write the truth value of the following statement:
∀ n ∈ N, n + 6 > 8.
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.
You are amazing!
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.
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
He is an actor.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 is a 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 π is an irrational number.
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.
Can you speak in English?
Choose the correct alternative :
Which of the following is an open statement?
The negation of the proposition “If 2 is prime, then 3 is odd”, is ______
Choose the correct alternative:
Which of the following is always true?
State whether the following statement is True or False :
x2 = 25 is true statement.
Solve the following :
State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.
Solve the following :
State which of the following sentences are statements in logic.
The square of any odd number is even.
Solve the following :
State which of the following sentences are statements in logic.
All integers are natural numbers.
Solve the following :
State which of the following sentences are statements in logic.
What a horrible sight it was!
Which of the following sentence is a statement? In case of a statement, write down the truth value.
The square of every real number is positive.
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.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 1
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.
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 (p ˅ ∼p)
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
If statements p, q are true and r, s are false, determine the truth values of the following.
(p ∧ ~r) ∧ (~q ∨ s)
Choose the correct alternative :
Which of the following is not a statement?
The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.
State whether the following statement is True or False:
(p ˅ q) ˄ ~ p is a contradiction
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
State whether the following statement is True or False:
Mathematical identities are true statements
State whether the following statement is True or False:
p ˅ ~ p ≡ ~ c
The truth value of negation of “London is in England” 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)
Which of the following quantified statement is true?
The negation of 'For every real number x, `x^2 ≥ 0`' is ______
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.
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.
If p : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.
lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12