(a)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.

Show that the statement p:"If x is a real number such that x^3+4x=0 then x is 0" is true by method of contrapositive.

Show that the statement p:"If x is a real number such that x^3+4x=0 then x is 0" is true by Direct method.

Show that the statement p:"If x is a real number such that x^3+4x=0 then x is 0" is true by Method of contradiction.

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

Consider the binary operation ast on the set R of real numbers, defined by aastb=a b /4 Show that ast is commutative and associative.

If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum value of b is

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

Let R be a .relation from Q to Q defined by R={(a, b): a, b in Q and a-b in Z }. Show that i) (a, a) in R for all a in Q ii) (a, b) in R implies that (b, a) in R iii) (a, b) in R and (b, c) in R implies that (a, c) in R .

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