Advertisements
Advertisements
प्रश्न
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
Advertisements
उत्तर
~ p ∧ (q ∨ ~ r)
≡ ∼T ∧ (T ∨ ∼ F)
≡ F ∧ (T ∨ T)
≡ F ∧ T
≡ F
∴ Truth value of ~ p ∧ (q ∨ ~ r) is F
APPEARS IN
संबंधित प्रश्न
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
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.
5 + 4 = 13
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.
x2 = x
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x2 – 6x – 7 = 0, when x = 7
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)
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
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 x2 < 0
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x is an even number.
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
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.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
If x is a whole number then x + 6 = 0.
`sqrt5` is an irrational but `3sqrt5` is a complex number.
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.
(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.
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.
The number 2 is the only even prime number.
Which of the following statements is false?
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” 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 :
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.
Ice cream Sundaes are my favourite.
Solve the following :
State which of the following sentences are statements in logic.
Why are you sad?
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.
What are the causes of rural unemployment?
Determine the truth value of the following statement.
4 + 5 = 7 or 9 − 2 = 5
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)
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 is any statement then ( p ˅ ∼ p) is a
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
State whether the following statement is True or False:
p ˅ ~ p ≡ ~ c
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
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 p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.
