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

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

If a ** b = sqrt(a^(2) + b^(2)) on the real numbers then ** is

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.

In a set of real numbers an operations * defined by a * b=sqrt(a^(2) +b^(2)) . Then the value of (3 * 5) * 4 is:

By giving a counter example, show that the following statements are not true. (ii) q: The equation x^(2) - 1 = 0 does not have a root lying between 0 and 2.

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

Find counter examples to disprove the following statements: For any integers x and y, sqrt(x^(2) + y^(2)) = x+y

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .