Advertisements
Advertisements
Question
By giving a counter example, show that the following statements are not true.
q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.
Advertisements
Solution
The given statement is as follows.
q: The equation x2 – 1 = 0 does not have a root lying between 0 and 2.
This statement has to be proved false. To show this, a counter example is required.
Consider x2 – 1 = 0
x2 = 1
x = ± 1
One root of the equation x2 – 1 = 0, i.e. the root x = 1, lies between 0 and 2.
Thus, the given statement is false.
APPEARS IN
RELATED QUESTIONS
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by
(i) direct method
(ii) method of contradiction
(iii) method of contrapositive
Find out the following sentence is a statement and is not. Justify your answer.
Listen to me, Ravi !
Find out the sentence are statement and are not. Justify your answer.
Every rhombus is a square.
Find out the sentence are statement and are not. Justify your answer.
There are 35 days in a month.
Write the negation of the statement:
Ravish is honest.
Some even integers are prime.
Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
There exist real numbers a and b for which a + b = b + a.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
A lady gives birth to a baby boy or a baby girl.
Determine whether the compound statement are true or false:
Delhi is in India and 2 + 2 = 4.
Write the negation of statement:
For every x ϵ N, x + 3 < 10
Write of the statement in the form "if p, then q".
The game is cancelled only if it is raining.
Check the validity of the statement:
p : 100 is a multiple of 4 and 5.
Identify the component statements and the connective in the following compound statements.
It is raining or the sun is shining.
Write the truth value of the following statements.
(i) 9 is an even integer or 9 + 1 is even.
(ii) 2 + 4 = 6 or 2 + 4 = 7
(iii) Delhi is the capital of India and Islamabad is the capital of Pakistan.
(iv) Every rectangle is a square and every square is a rectangle
(v) The sun is a star or sun is a planet.
Rewrite the following statements in the form of conditional statements:
Ramesh will get dessert only if he eats his dinner.
Rewrite the following statements in the form of conditional statements:
A necessary condition for Indian team to win a cricket match is that the selection committee selects an all-rounder.
Express in English, the statement p → q, where
p: It is raining today
q: 2 + 3 > 4
Translate the following statements in symbolic form:
If x = 7 and y = 4” then x + y = 11.
Which of the following is a statement?
Which of the following sentences are statements? Justify
0 is a complex number.
Which of the following sentences are statements? Justify
15 + 8 > 23
Find the component statements of the following compound statements.
The number 100 is divisible by 3, 11 and 5.
Find the component statements of the following compound statements.
Chandigarh is the capital of Haryana and U.P.
Write down the negation of following compound statements
x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.
Write down the negation of following compound statements
35 is a prime number or a composite number
Write down the negation of following compound statements
All prime integers are either even or odd.
Rewrite the following statements in the form of conditional statements
The unit digit of an integer is 0 or 5 if it is divisible by 5.
Form the biconditional statement p ↔ q, where
p: A natural number n is odd.
q: Natural number n is not divisible by 2.
Identify the Quantifiers in the following statements.
For all real numbers x and y, xy = yx.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
The negation of the statement “Rajesh or Rajni lived in Bangalore” is ______.
Which of the following is not a negation of “A natural number is greater than zero”?
