For any two sets A and B, \(A\cap(A\cup B)=\)_____.

If \(A\cap B=B\) then _____.

If A = {1, 2, 3, 4, 5, 6}then the number of proper sub-sets is _____.

If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5} then A - B is _____.

In a set builder method, the null set is represented by _____.

If U={a,b,c,d,e,f}, A={a,b,c}, B={c,d,e,f}, C={c,d,e}, D={d,e,f}, then tabulate the following set A\(\cap \)C

Let A = {x :x \(\in\) N}, B= {x : x= 2n, n\(\in\)N, C={x : x = 2n-1, n\(\in\)N} and D= {x :x is a prime natural number}. Find  A\(\cap\)C

Let A = {x :x \(\in\) N}, B= {x : x= 2n, n\(\in\)N, C={x : x = 2n-1, n\(\in\)N} and D= {x :x is a prime natural number}. Find B\(\cap\)C

Which of the following are sets? Justify your answer:
The collection of all odd integers.

Let A, B, C be three sets. If A ∈ Band B ⊂ C, is it true that A ⊂ C?
[Hint: Take A={1},B={{1},2} and C={{1},2,3}]

From the following sets given below, pair the equivalent sets.
A= {1, 2, 3}, B= {t, p, q, r, s}, C= {\(\alpha ,\beta ,\gamma \)} and D= {a, e, i, o, u}

If X and Y are two sets such that X has 40 elements, X \(\cup \)Y has 60 elements and X\(\cap \)Y has 10 elements, then how many elements does Y have?
Use the formula, n(A\(\cup \)B)=n(A)+n(B)-n(A\(\cap \)B) and simplify it

Which of the following sets are finite and which are infinite?
The set of animals living on the Earth.

In a group of 50 people, 30 like to play cricket, 25 like to play football and 32 like to play hockey. Assume that each person in the group likes to play at least one of the three games. If 15 people like to play both cricket and football, 11 like to play football and hockey and 18 like to play cricket and hockey. Find:
(i) How many like to play all three games?
(ii) How many like to play only football?
(iii)How many like to play only hockey?
(iv) How many like to play exactly one game?

Each student in a class of 40, reads atleast one of the subjects Hindi, English and Sanskrit. 16 students read Hindi, 22 read Sanskrit and 26 read English. 5 read Hindi and Sanskrit, 14 read English and Sanskrit and 2 read the three languages. Find the number of students who read.
(i) Hindi and English
(ii) Hindi, English but not Sanskrit.

If X={1,2,3} and n represents any member of X, write the following sets containing all numbers represented by \(\frac { n }{ 2 } \)

If X={1,2,3} and n represents any member of X, write the following sets containing all numbers represented by n-1

Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A
(ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A
(v) 1⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) ¢ ∈ A
(x) ¢⊂ A
(xi) {¢} ⊂ A.

Draw the Venn diagrams to illustrate the following relationship among sets, E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
Some of the students study Mathematics but do not study English, some study English but do not study Mathematics, and some study both.