Advertisements
Advertisements
प्रश्न
Show that the statement “For any real numbers a and b, a2 = b2 implies that a = b” is not true by giving a counter-example.
Advertisements
उत्तर
The given statement can be written in the form of “if-then” as follows.
If a and b are real numbers such that a2 = b2, then a = b.
Let p: a and b are real numbers such that a2 = b2.
q: a = b
The given statement has to be proved false. For this purpose, it has to be proved that if p, then ∼q. To show this, two real numbers, a and b, with a2 = b2 are required such that a ≠ b.
Let a = 1 and b = –1
a2 = (1)2 = 1 and b2 = (– 1)2 = 1
∴ a2 = b2
However, a ≠ b
Thus, it can be concluded that the given statement is false.
APPEARS IN
संबंधित प्रश्न
Find out the sentence are statement and are not. Justify your answer.
The cat pussy is black.
Find out the sentence are statement and are not. Justify your answer.
This sentence is a statement.
Find out the sentence are statement and are not. Justify your answer.
Go !
Find out the sentence are statement and are not. Justify your answer.
Mathematics is difficult.
Write the negation of the statement:
Banglore is the capital of Karnataka.
Both the diagonals of a rectangle have the same length.
Are the pair of statement are negation of each other:
The number x is not a rational number.
The number x is not an irrational number.
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.
Find the component statement of the compound statement:
All rational numbers are real and all real numbers are complex.
For statement, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.
Students can take Hindi or Sanskrit as their third language.
Determine whether the compound statement are true or false:
Delhi is in England and 2 + 2 =5.
Negate statement:
All the students completed their homework.
Write of the statement in the form "if p, then q".
It is necessary to have a passport to log on to the server.
statement are true and false? In each case give a valid reason for saying so
s : If x and y are integers such that x > y, then − x < − y.
Translate the following statements in symbolic form
Tigers are found in Gir forest or Rajaji national park.
Write the negation of the following statements:
q: 9 is a multiple of 4.
Rewrite the following statements in the form of conditional statements:
Mohan will be a good student if he studies hard.
Rewrite the following statements in the form of conditional statements:
A sufficient condition for Tara to visit New Delhi is that she goes to the Rashtrapati Bhawan.
Identify the quantifiers and write the negation of the following statements:
For all even integers x, x2 is also even.
Check the validity of the statements:
s: 60 is a multiple of 3 or 5.
Which of the following sentences are statements? Justify
15 + 8 > 23
Which of the following sentences are statements? Justify
Where is your bag?
Translate the following statements into symbolic form
Students can take Hindi or English as an optional paper.
Write down the negation of following compound statements
All prime integers are either even or odd.
Write down the negation of following compound statements
6 is divisible by 2 and 3.
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.
Rewrite the following statements in the form of conditional statements
2b = a + c, if a, b and c are in A.P.
Identify the Quantifiers in the following statements.
There exists a triangle which is not an isosceles triangle.
Identify the Quantifiers in the following statements.
There exists a real number x such that x2 + 1 = 0.
Check the validity of the following statement.
q: 131 is a multiple of 3 or 11
Which of the following is a statement?
The connective in the statement “2 + 7 > 9 or 2 + 7 < 9” is ______.
The connective in the statement “Earth revolves round the Sun and Moon is a satellite of earth” is ______.
The negation of the statement “Plants take in CO2 and give out O2 ” is ______.
Which of the following statement is a conjunction?
State whether the following sentences are statements are not.
(i) The angles opposite to equal sides of a triangle are equal.
(ii) The moon is a satellite of earth.
(iii) May God bless you!
(iv) Asia is a continent.
(v) How are you?
