MENU
Question -

Show that the statement “For anyreal numbers a and b, a2 = b2 impliesthat a = b” is not true by giving acounter-example.



Answer -

The given statement can bewritten in the form of “if-then” as follows.

If a and b arereal numbers such that a2 = b2,then a = b.

Let p: a and b arereal numbers such that a2 = b2.

q: a = b

The given statement has to beproved false. For this purpose, it has to be proved that if p, then∼q. To showthis, two real numbers, a and b, with a2 = b2 arerequired such that a ≠ b.

Let a = 1and b = –1

a2 =(1)2 = 1 and b2 = (– 1)2 =1

∴ a2 = b2

However, a ≠ b

Thus, it can be concluded thatthe given statement is false.

Comment(S)

Show all Coment

Leave a Comment

Free - Previous Years Question Papers
Any questions? Ask us!
×