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.

By giving a conter example , show that the statement " For any real number a and b a^(2) =b^(2) rArr a= b" is false

a ** b = a^(b) AA a, b in Z . Show that * is not a binary operation on Z by giving a counter example.

Show that the binary operation * defined on R by a ** b = (a + b)/2 is not associative by giving a counter example.

For any two real numbers, an operation * defined by a *b = 1 + ab is

If a, b and c real numbers such that a^(2) + b^(2) + c^(2) = 1, then ab + bc + ca lies in the interval :

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

For any two real numbers, an operation ** defined by a**b=1+ab is

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

In Boolean algebra A + B = Y implies that :

Show that the relation S in the set R of real numbers defined as S={(a,b): a, b in R and a le b^(3) } is neither reflexive, nor symmetric, nor transitive.