Question -
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.