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
If p ˄ q = F, p → q = F, then the truth value of p and q is ______.
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
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.
4 is odd or 1 is prime.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
Write the truth value of the following.
Milk is white if and only if sky is blue.
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 → s)
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:
4! = 24.
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
∃ n ∈ N such that n + 5 > 10.
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.
`sqrt(-4)` 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.
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.
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.
If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.
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 statements is false?
Choose the correct alternative :
The statement (∼ p ∧ q) ∨∼ q is
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
Fill in the blanks :
Truth value of if x = 2, then x2 = − 4 is –––––––––.
Fill in the blanks :
Truth value of 2 + 3 = 5 if and only if − 3 > − 9 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 :
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 :
“His birthday is on 29th February” is not a 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.
Do not come inside the room.
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.
Please carry out my instruction.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
What are the causes of rural unemployment?
Determine the truth value of the following statement.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 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)
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 + 2 ≥ 5.
State the truth value of `sqrt(3)` is not an irrational number
If statements p, q are true and r, s are false, determine the truth values of the following.
(p ∧ ~r) ∧ (~q ∨ s)
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
If q Λ ∼p is T, then which of the following is correct?
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.
