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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. - Mathematics and Statistics

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प्रश्न

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.

एक पंक्ति में उत्तर
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उत्तर

It is a statement which is true, hence its truth value is ‘T’.

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अध्याय 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ८]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.1 | Q 1.08 | पृष्ठ ८

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संबंधित प्रश्न

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

Zero is a complex number.


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.

The sunsets in the west


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

The sum of cube roots of unity is zero.


Write the truth values of the following.

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


Write the truth value of the following.

Milk is white if and only if sky is blue.


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 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 such that x – 8 = 1


Write the truth value of the following statement:

∃ n ∈ N such that n + 5 > 10.


Write the truth value of the following statement:

In ΔABC if all sides are equal then its all angles are equal.


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.

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.

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.

Bring the motor car here.


Choose the correct alternative :

Which of the following is an open statement?


Which of the following statements is false?


The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


Choose the correct alternative:

Which of the following is always true?


Choose the correct alternative :

∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to


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


Choose the correct alternative :

Conditional p → q is equivalent to


Fill in the blanks :

The statement q → p is called as the ––––––––– of the statement p → q.


State whether the following statement is True or False :

Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.


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.
x + 3 = 8 ; x is variable.


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.
(2 + 1)2 = 9.


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.


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

∃ x ∈ A, such that x + 3 < 11.


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


The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______


Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)


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`


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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`


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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.


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


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