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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

If p is any statement then ( p ˅ ∼ p) is a - Mathematics and Statistics

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प्रश्न

If p is any statement then ( p ˅ ∼ p) is a

पर्याय

  • Contingency

  • Contradiction

  • Tautology

  • None of these

MCQ
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उत्तर

Tautology

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पाठ 1.1: Mathematical Logic - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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.

5 + 4 = 13


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.

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)] ∨ [(q ∧ r) ∨ (p ∧ r)]


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)


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, x is an even number.


Write the truth value of the following statement:

∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.


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.

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 π 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.

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.


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.


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 :

If p is the sentence ‘This statement is false’ then


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 :

x2 = 25 is true statement.


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.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


Solve the following :

State which of the following sentences are statements in logic.
(2 + 1)2 = 9.


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.
If x is real number then x2 ≥ 0.


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.

Please carry out my instruction.


Determine the truth value of the following statement.

If 9 > 1 then x2 − 2x + 1 = 0 for x = 1


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 A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∀ x ∈ A, x2 < 18.


If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∀ x ∈ A, x2 + 2 ≥ 5.


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 ______


If (p ∧ ~ q) → ~ p is false, 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).


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


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