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Choose the correct alternative : Which of the following statement is true? - Mathematics and Statistics

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प्रश्न

Choose the correct alternative :

Which of the following statement is true?

विकल्प

  • 3 + 7 = 4 or 3 – 7 = 4

  • If Pune is in Maharashtra, then Hyderabad is in Kerala

  • It is false that 12 is not divisible by 3

  • The square of any odd integer is even

MCQ

उत्तर

It is false that 12 is not divisible by 3

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अध्याय 1.1: Mathematical Logic - Q.1

संबंधित प्रश्न

If p ˄ q = F, p → q = F, then the truth value of p and q is ______.


Write the truth values of the following.

64 is a perfect square and 46 is a prime number.


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

∃ x ∈ A such that x – 8 = 1


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

∀ x ∈ A, x is an even number.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

π is an irrational number.


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.


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.

It may rain today.


Choose the correct alternative :

Negation of the statement “This is false or That is true” is


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.
All integers are natural numbers.


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 square of every real number is positive.


Determine the truth value of the following statement.

x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.


The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.


State whether the following statement is True or False:

(p ˅ q) ˄ ~ p is a contradiction


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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