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Solve the following : State which of the following sentences are statements in logic.The square of any odd number is even. - Mathematics and Statistics

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प्रश्न

Solve the following :

State which of the following sentences are statements in logic.
The square of any odd number is even.

विकल्प

  • Is a statement

  • Is not a statement

MCQ
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उत्तर

Is a statement

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३१]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.01 | पृष्ठ ३१

संबंधित प्रश्न

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex 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.

Congruent triangles are similar.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

All real numbers are whole numbers.


Write the truth values of the following.

5 is a prime number and 7 divides 94.


Write the truth values of the following.

It is not true that 5−3i is a real number.


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, 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


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, 2x + 9 > 14


If p ∧ q is F, p → q is F then the truth values of p and q are ________.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The sum of interior angles of a triangle is 180°


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Please grant me a loan.


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.

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.

The number 2 is the only even prime number.


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 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 :

x2 = 25 is true statement.


Solve the following :

State which of the following sentences are statements in logic.
What a horrible sight it was!


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4 + 5 = 7 or 9 − 2 = 5


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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.


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∀ x ∈ A, x2 + 2 ≥ 5.


State the truth Value of x2 = 25


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Which of the following is not a statement?


If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.


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.


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Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


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