Write the set of letters of the following words in Roster form
PRINCIPAL

Find the number of subsets and the number of proper subsets of a set X = {a, b, c, x, y, z}.

If U = {c, d, e, f, g, h, i, j} and A = { c, d, g, j} , find A′.

Represent A Δ B through Venn diagram.

Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.

Draw Venn diagram and shade the region representing the following sets
(A – B)′

In a party of 60 people, 35 had Vanilla ice cream, 30 had Chocolate ice cream. All the people had at least one ice cream. Then how many of them had,
(i) both Vanilla and Chocolate ice cream.
(ii) only Vanilla ice cream.
(iii) only Chocolate ice cream.

If n(A) = 25, n(B) = 40, n(A∪B) = 50 and n(B′) = 25 , find n(A∩B) and n(U).

Let U = {0, 1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets. (B′)′

Using the set symbols, write down the expressions for the shaded region in the following

Let A and B be two overlapping sets and the universal set be U. Draw appropriate Venn diagram for each of the following,
(i) AUB
(ii) A∩B
(iii) (A∩B)′
(iv) (B–A)'
(v) A′UB′
(vi) A′∩B′
(vii) What do you observe from the Venn diagram (iii) and (v)?

Write the following in "Roster" form?
(a) A = set of the months having 31 days.
(b) B = {x : x is a natural number of 2 digits divisible by 13}
(c) C = {set of vowels in the word "father"}
(d) D = {x : 5 < x < 10 ; x ∈ N}
(e) E = {x: x is a square natural number less than 16}

In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics only

Represent U= {1,2,3,4,5,6,7,8,9,10} A = {1,2,4,6,8,10} and B = {3,6,1,10} in venn-diagram, then find
(i) (A UB)'
(ii) (A ∩ B)'

IfA = {1,2,3} B = {3,5,6} C = {3,4,7}. Find
(i) A-(BUC)
(ii) BΔC
(iii) AΔB