Advertisements
Advertisements
प्रश्न
Write the truth values of the following.
5 is a prime number and 7 divides 94.
उत्तर
Let p: 5 is a prime number.
q: 7 divides 94.
Then the symbolic form of the given statement is p∧q.
The truth values of p and q are T and F respectively.
∴ The truth value of p∧q is F .........[T∧F ≡ F]
APPEARS IN
संबंधित प्रश्न
If p ˄ q = F, p → q = F, then the truth value of p and q is ______.
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.
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.
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.
The sunsets in the west
Write the truth values of the following.
24 is a composite number or 17 is a prime number.
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 such that 3x + 8 > 40
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:
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:
Please get me a glass of water.
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:
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.
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.
Every real number is a complex number.
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.
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.
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.
Can you speak in English?
Which of the following is not a statement?
Which of the following statements is false?
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
Fill in the blanks :
Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r 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 :
p ∨ q has truth value F is both p and q has truth value F.
Solve the following :
State which of the following sentences are statements in logic.
x + 3 = 8 ; x is variable.
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.
All integers are natural numbers.
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.
(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.
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
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high and stocks are rising if and only if stock prices are high.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
It is false that stocks are rising and stock prices are high.
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 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, x2 < 18.
If p is any statement then ( p ˅ ∼ p) is a
State the truth value of `sqrt(3)` is not an irrational number
State the truth Value of x2 = 25
State the truth value of (p ˅ ∼p)
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 ∧ ~r) ∧ (~q ∨ s)
Choose the correct alternative :
Which of the following statement is true?
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:
Truth value of `sqrt(3)` is not an irrational number is F
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
The truth value of negation of “London is in England” is ______
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Which of the following quantified statement is true?
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 ______.
If q Λ ∼p is T, then which of the following is correct?
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.
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)`.
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12