Advertisements
Advertisements
प्रश्न
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 + 2 ≥ 5.
Advertisements
उत्तर
∀ x ∈ A, x2 + 2 ≥ 5.
x = 2; 22 + 2 ≥ 5
∵ for all given values of
x = 2, 3, 4, 5, 6, 7, 8
x2 + 2 ≥ 5 condition satisfied.
∴ The truth value of the given statement is True (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.
x2 = x
Write the truth values of the following.
64 is a perfect square and 46 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 ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)
Write the truth value of the following statement:
In ΔABC if all sides are equal then its all angles are equal.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 - y2 = (x + y)(x - y) for all x, y ∈ R.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Two co-planar lines are either parallel or intersecting.
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.
Which of the following statements is false?
Choose the correct alternative :
For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.
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?
Choose the correct alternative :
Negation of the statement “This is false or That is true” is
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.
Fill in the blanks :
p ↔ q is false when p and q have ––––––––– truth values.
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 :
x2 = 25 is true statement.
State whether the following statement is True or False :
p ∧ t = p.
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.
If x is real number then x2 ≥ 0.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
0! = 1
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)]
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
Which of the following quantified statement is true?
Let a: ~ (p ∧ ~ r) v (~ q v s) and
b: (p v s) ↔ (q ∧ r).
If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.
If p ↔ (~ 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.
