Sets (Advanced)

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   A set A has 8 elements. How many elements does its power set P(A) have?

   1. 64
   2. 16
   3. 255
   4. 256

   Answer

   (d) 256

   n[P(A)] = 2⁸ = 256

2. 2.

   Of 48 people, 37 drink tea, 30 drink coffee and 1 do neither. How many do both?

   1. 17
   2. 10
   3. 21
   4. 20

   Answer

   (d) 20

   n(A ∪ B) = 48 − 1 = 47; n(A ∩ B) = 37 + 30 − 47 = 20

3. 3.

   The empty set φ is a subset of:

   1. only infinite sets
   2. no set at all
   3. only the empty set
   4. every set

   Answer

   (d) every set

   φ has no element that could fail to be in another set

Section B · short answer

1. 4.

   U = {1, 2, …, 16}, A = {1, 9, 13, 15, 16} and B = {1, 3, 8, 9, 12, 13}. Find A ∪ B, A ∩ B, A − B and (A ∪ B)′.

   Answer

   A ∪ B = {1, 3, 8, 9, 12, 13, 15, 16}; A ∩ B = {1, 9, 13}; A − B = {15, 16}; (A ∪ B)′ = {2, 4, 5, 6, 7, 10, 11, 14}

   (A ∪ B)′ is everything in U outside A ∪ B

2. 5.

   Write the power set of {d, x, z}. How many proper subsets does the set have?

   Answer

   P = {φ, {d}, {x}, {z}, {d, x}, {d, z}, {x, z}, {d, x, z}}; 7 proper subsets

   2³ = 8 subsets; all but the set itself are proper: 8 − 1 = 7

Section C · long answer

1. 6.

   In a group of 51 students, 10 play cricket, 3 of these also play football, and 20 do neither of the two. Find how many (a) play football (b) play football but not cricket (c) do exactly one of the two.

   Answer

   (a) 24; (b) 21; (c) 28

   n(A ∪ B) = 51 − 20 = 31; n(B) = 31 − 10 + 3 = 24; only B = 24 − 3; exactly one = 7 + 21

Fresh sheets for your child

In the app, every Sets (Advanced) sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

Coming soon for Android and iPhone.

More Class 9 Mathematics