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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° - Mathematics and Statistics

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प्रश्न

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°

एक पंक्ति में उत्तर
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उत्तर

It is a statement which is true. Hence, it’s truth value is T.

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अध्याय 1: Mathematical Logic - Exercise 1.1 [पृष्ठ २]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.1 | Q 2 | पृष्ठ २

संबंधित प्रश्न

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


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

5 + 4 = 13


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 ∧ r) ∨ (p ∧ r)]


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

∀ x ∈ A, 2x + 9 > 14


If A = {1, 2, 3, 4, 5} then which of the following is not true?


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

π is an irrational number.


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.


Write the truth value of the following statement:

∀ n ∈ N, n + 6 > 8.


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.

x2 − 6x + 8 = 0 implies x = −4 or x = −2.


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.


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.


If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.


Fill in the blanks :

p ↔ q is false when p and q have ––––––––– truth values.


Solve the following :

State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.


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.

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


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 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, x2 < 18.


State the truth value of (p ˅ ∼p)


Choose the correct alternative :

Which of the following statement is true?


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˄ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`

p ˄ q

i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square`

ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square`


Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number

Write truth values by activity

i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square`

= `square` ˄ `square`

= `square`

ii) ~ ( p ˄ r ) = `~(square` ˄ `square)`

= `~ square`

= `square`

iii) p → q = `square → square`

= `square`


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.


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