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.

IF x and be are real numbers and b>0,|x|>b then

By giving a counter example show that the following compound statement is not true . "If x and y are two real numbers , then x^(2)=y^(2) implies x = y " .

If 2 (a ^(2) + b ^(2)) = (a+b)^(2), then show that a =b

If a,b,c are distinct positive real numbers and a^(2)+b^(2) +c^(2)=1 then the value of ab+bc+ca is-

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

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

If three positive real number a,b and c are in G.P show that log a , log b and log c are in A.P

For any two sets A and B, if A cupB = A cap B , then show that A = B.

Show that the relation R in the set R of real numbers, defined as R = {(a,b) : a le b ^(2)} is neither reflexive nor symmetric nor transitive.

Show that the relation R in the set R of real numbers, defined as R={(a ,b): alt=b^2} is neither reflexive nor symmetric nor transitive.