Is the set {x:x + a = a for all a `in`R}, a singleton set?

If sec (1/x) = cos^-1 x for all x in A, then find the set A.

Let N be the universal set. Write the complement of the following set : {x: x in N and x = 3n for some n in N}.

If cot^-1 x = tan^-1(1/x) for all x in S, then find the set S.

Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60^@ , what is A'?

If cosec^-1 x = sin^-1 (1/x) for all x in S , then find the set S.

Show that the relation R in the set : R = {x : x in Z, 0 le x le 1 2}, given by : R = {(a, b): a = b} are equivalence relations.

Let ** be a binary operation on the set of all non-zero real numbers, given by a **b=(ab)/5 for all a, b in R- {0} . Find the value of x, given that 2 ** (x **5) = 10

Taking the set of natural numbers as the universal set, write down the complements of the following set: {x : x is a natural number divisible by 3 and 5}

The set {x:x is an integer and -3 < x le 2 } is equal to:

What is the set : {x:x in R, x^2=9, 2x=4} ?