Advertisements
Advertisements
प्रश्न
If p is any statement then ( p ˅ ∼ p) is a
पर्याय
Contingency
Contradiction
Tautology
None of these
उत्तर
Tautology
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.
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.
Close the door.
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.
Do you like Mathematics?
Write the truth values of the following.
64 is a perfect square and 46 is a prime number.
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:
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:
[(∼ p ∧ q) ∧ ∼ r] ∨ [(q → p) → (∼ s ∨ r)]
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x – 8 = 1
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:
∃ 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.
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.
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.
Have a cup of cappuccino.
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.
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.
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.
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.
Choose the correct alternative :
∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to
Fill in the blanks :
Truth value of if x = 2, then x2 = − 4 is –––––––––.
State whether the following statement is True or False :
Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.
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.
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.
Read a lot to improve your writing skill.
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.
Solve the following :
State which of the following sentences are statements in logic.
What a horrible sight it was!
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.
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
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.
If stock prices are high then stocks are not rising.
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 ∧ 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, such that 3x + 2 > 9
Which of the following statement is true
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)
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:
p → q is equivalent to p → ~ q
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:
Mathematical identities are true statements
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.
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.
lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).
