Show that the set of letters needed to spell “ CATARACT ” and the set of letters needed to spell “ TRACT” are equal.

Let A be the set of prime numbers smaller than 6 and p the set of prime factors of 30. Check if A and P are equal.

Write the following sets in roster form. E = {the set of all letters in the word BETTER}.

Write the following sets in roaster form D = { the set of all letters in the word CRICKET}

Show that A ∩ B = A ∩ C need not imply B = C .

Write the following sets in roster form: E = The set of all letters in the word TRIGONOMETRY

Consider a set of vowels letters , V = {a, e, i, o, u}. Also consider the set A, of all letters in the English alphabet. A = {a, b, c, d, ….., z}. Identify the universal set and the subset in the given example.

State whether each of the following sets is finite or infinite. The set of letters in the English alphabet.

Show that the relation R in the set A of points in a plane given by R = {(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.