The number of subsets of a set containing n elements is _____.

If \(A\cap B=B\) then _____.

If A and B are two sets then A \(\cap\) (A \(\cap\) B') =_______.

Let U be the universal set containing 700 elements. If A and B are sub-sets of U such that n(A) = 200, n(B) = 300 and n(A \(\cap\) B) = 100, then n(A' \(\cap\) B') =___.

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

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 (U\(\cup \)A)'

Let A ={x :x ia natural number } and B ={x :x is an even number}. Find A\(\cap\)B.

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 A = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then insert appropriate symbol ∈∈ or ∉∉ in each of the following blank space.
9 ... A

Are the following pair of sets equal? Give reason.
A = {2, 3} and B = {x : x is a solution of x² + 5x + 6 = 0}

Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in  English and Mathematics but not in Science?

If n(A)=4, n(B)=6, then what can be the minimum number of elements in A\(\cup \) B?

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.

Show that for any sets A and B, A = (A \(\cap\) B) \(\cup\) (A-B) and A \(\cup\) (B-A)=(A \(\cup\) B).