मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

Advertisements
Advertisements

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.

एका वाक्यात उत्तर

उत्तर

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

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ८]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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.

Zero is a complex number.


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

x2 = x


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.

All real numbers are whole numbers.


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

x2 – 6x – 7 = 0, when x = 7


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 value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.


Write the truth value of the following.

Milk is white if and only if sky is blue.


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 → s)


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

(q ∧ r) ∨ (∼ p ∧ s)


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 → 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, x2 + x is an even number


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

∃ x ∈ A such that x2 < 0


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

∃ x ∈ A such that 3x + 8 > 40


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:

4! = 24.


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

If x is a whole number then x + 6 = 0.


`sqrt5` is an irrational but `3sqrt5` is a complex 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.

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.

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.

Did you eat lunch yet?


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.


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.

It may rain today.


Which of the following is not a statement?


Choose the correct alternative :

For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.


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


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 :

p ∨ q has truth value F is both p and q has truth value F.


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.
Read a lot to improve your writing skill.


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.
Why are you sad?


Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.


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.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

Every parallelogram is a rhombus.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

What are the causes of rural unemployment?


Which of the following sentence is a statement? In case of a statement, write down the truth value.

The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.


Determine the truth value of the following statement.

4 + 5 = 7 or 9 − 2 = 5


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)


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 x2 = 25


If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)


If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)


Choose the correct alternative :

Which of the following statement is true?


Choose the correct alternative :

Which of the following is not a statement?


State whether the following statement is True or False:

Mathematical identities are true statements


Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p


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`


Which of the following quantified statement is true?


If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.


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


If p `rightarrow` (p ∧ ∼q) is false, 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).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×