Home
Class 11
MATHS
Show that the statement For any real num...

Show that the statement For any real numbers `a\ a n d\ b ,\ a^2=b^2` implies that `a=b` is not true by giving a counter example

Text Solution

Verified by Experts

Given statement : for any real numbers a and b , `a^2=b^2` implies that `a=b` , is not true.
Let `a=4` and `b=-4` then `aneb`
`rArra^2=16` and `b^2=16rArra^2=b`
so, `aneb` and `a^2=b^2`
therefore,given statement is not true.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN|Exercise Misellaneous exercise|7 Videos
  • MATHEMATICAL REASONING

    NAGEEN PRAKASHAN|Exercise Exercise 14.4|4 Videos
  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN|Exercise MISCELLANEOUS EXERCISE|14 Videos
  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|11 Videos

Similar Questions

Explore conceptually related problems

Show that the statement For any real numbers a and b,a^(2)=b^(2) implies that a=b is not true by giving a counter example

Show that the statement For any real numbers a and b,a^(2)=b^(2) implies that is not true by giving a counter-example.

For any two real numbers a and b, sqrt((a-b)^2)+sqrt((b-a)^2) is

For any whole numbers a, b, c is it true that (a+b)+c=a+(c+b) ? Give reasons.

For any two real numbers a and b,we define a R b if and only if sin^(2)a+cos^(2)b=1. The relation R is

By giving a counter example,show that the following statement is not true: p: if all the angles of a triangle are equal,then the triangle is an obtuse angled triangle.

If a, b and c are real numbers such that a < b and clt0 , then of the statements which is true?

Let A,B and C be three sets.If A in B and is it true that is it true that ? If not give an example.