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

In Boolean algebra A + B = Y implies that :

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

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

If A and B are any two sets, prove that P(A) = P(B) implies A = B.

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.

For any three positive real numbers a , b and c ,9(25 a^2+b^2)+25(c^2-3a c)=15 b(3a+c)dot Then :

True statement about hepatitis B vaccine is

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