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

Write the set of the letter of the word 'ALLAHABAD'. Also find the number of subsets of this set.

Let A be the set of prime number smaller than 6 and B be the set of prime factors of 30. Check if A and B are equal.

Which of the following pairs of sets are equal? Justify your answer. (i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”. (ii) A = {n : n ∈ Z and n^(2) ≤ 4} and B = {x : x ∈ R and x^(2) – 3x + 2 = 0} .

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

Write the following sets in roster form: F = The set of all letters in the word BETTER

State whether the followmg sets are finite or infinite. (i) The set of months in a year. (ii) {1,2,3, ..., 99, 100) (iii) The set of prior numbers smaller than 99. (iv) The set of letters in the English alphabet. (v) The set of lines that can be drawn are parallel to the X-Axis (vi) The set of numbers which are muitiplies of 5. (vii) The set of circles passing through the origin (0,0).

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

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

A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.

Show that the set of all points such that the difference of their distances from (4,0) and (-4, 0) is always equal to 2 represent a hyperbola.