Advertisements
Advertisements
प्रश्न
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x – 8 = 1
Advertisements
उत्तर
This means there exists an element x in A such that x − 8 = 1. Solving for x:
∴ x − 8 = 1
∴ x = 1 + 8
∴ x = 9
Check if x = 9 belongs to A:
The set A = {3, 5, 7, 9, 11, 12} contains 9.
There exists an x ∈ A such that x − 8 = 1
Clearly x = 9 ∈ A satisfies x − 8 = 1. So the given statement is true, hence its truth value is T.
APPEARS IN
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.
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Congruent triangles are similar.
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.
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.
Can you speak in Marathi?
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.
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:
(q ∧ r) ∨ (∼ p ∧ s)
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, x2 + x is an even number
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
π is an irrational number.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
Please get me a glass of water.
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.
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.
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.
With the sunset the day ends.
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.
It may rain today.
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.
Ice cream Sundaes are my favourite.
Solve the following :
State which of the following sentences are statements in logic.
(2 + 1)2 = 9.
Solve the following :
State which of the following sentences are statements in logic.
Do not come inside the room.
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.
0! = 1
Which of the following sentence is a statement? In case of a statement, write down the truth value.
The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.
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.
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, such that x + 3 < 11.
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
State whether the following statement is True or False:
Truth value of `sqrt(3)` is not an irrational number is F
The truth value of negation of “London is in England” is ______
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
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` |
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
