English

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

Question

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.

One Line Answer
Advertisements

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.1 [Page 8]

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n2 + n is an even number and n2 - n is an odd number.


Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.


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.

Do you like Mathematics?


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


Write the truth values of the following.

5 is a prime number and 7 divides 94.


Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.


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:

(p → q) ∧ ∼ r


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.

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 π 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.

If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.


Choose the correct alternative:

Which of the following is always true?


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.


Fill in the blanks :

Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.


State whether the following statement is True or False :

There are 24 months in year is a statement.


State whether the following statement is True or False :

Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.


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.
The square of any odd number is even.


Solve the following :

State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.


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?


Determine the truth value of the following statement.

4 + 5 = 7 or 9 − 2 = 5


Determine the truth value of the following statement.

It is not true that 2 + 3 = 6 or 12 + 3 =5


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

∀ x ∈ A, x2 + 2 ≥ 5.


If p is any statement then ( p ˅ ∼ p) is a


State the truth value of `sqrt(3)` is not an irrational number


State the truth value of (p ˄ ∼p) 


Choose the correct alternative :

Which of the following is not a statement?


State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values


State whether the following statement is True or False:

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q


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


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`


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`


The negation of 'For every real number x, `x^2 ≥ 0`' is ______ 


If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.


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.


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×