Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Truth values of p and q are T and truth values of r and s are F.
(∼ r ↔ p) → (∼ q) ≡ ( ∼ F ↔ T) → (∼ T)
≡ (T ↔ T) →F
≡ T→ F ≡ F
Hence the truth value of the given statement is false.
APPEARS IN
संबंधित प्रश्न
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.
A quadratic equation cannot have more than two roots.
Write the truth values of the following.
It is not true that 5−3i is a real 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:
(q ∧ r) ∨ (∼ p ∧ s)
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, x2 + 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:
Please get me a glass of water.
Write the truth value of the following statement:
The square of any even number is odd or the cube of any odd number is odd.
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.
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.
(x + y)2 = x2 + 2xy + y2 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.
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.
3 + 5 > 11
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.
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.
Which of the following is not a statement?
Choose the correct alternative :
Which of the following is an open statement?
Which of the following statements is false?
Choose the correct alternative:
Which of the following is always true?
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) 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.
State whether the following statement is True or False :
“His birthday is on 29th February” is not a statement.
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.
The square of any odd number is even.
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.
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.
(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.
Determine the truth value of the following statement.
4 + 5 = 7 or 9 − 2 = 5
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.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
p ↔ (q → ∼ p)
State the truth Value of x2 = 25
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
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)
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.
