Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n.

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 4n

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.

Find the intersection of each pair of sets of question 1above.

Let A = {I, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, C = {2, 3, 4, 5}, Find.
(i) A - (B \(\cup\) C)
(ii) A-(B \(\cap\) C)
(iii) A \(\cap\) (B-C)
(iv) B-(A-C)

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.
There is no student who studies both Mathematics and English.
 

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.

In a survey of 25 students, it was found that 15 had taken mathematics, 12 had taken physics and 11 had taken chemistry. 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all the three subjects. Find the number of students who had
(i) only chemistry
(ii) only physics
(iii) only mathematics
(iv) physics and chemistry but not mathematics
(v) mathematics and physics but not chemistry
(vi) at least one of the three subjects.
(vii) only one of the subjects.
(viii) none of the subjects.