Sets, Short Questions (Question 1 - 4)


Question 1:
List all the subsets of set P = {r, s}.

Solution:
There are 2 elements, so the number of subsets of set P is 2n = 22 = 4.

Set P = {r, s}
Therefore subsets of set P = {r}, {s}, {r, s}, { }.



Question 2:

Diagram above shows a Venn diagram with the universal set, ξ = Q υ P.
List all the subset of set P.

Solution:
Set P has 3 elements, so the number of subsets of set P is 2n = 23 = 8.

Set P = {2, 3, 5}
Therefore subsets of set P = { }, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, 
                                               {2, 3, 5}.


Question 3:
It is given that the universal set, ξ = {x : 30 ≤ x < 42, x is an integer} and 
set P = {x : x is a number such that the sum of it its two digits is an even 
number}.
Find set P’.

Solution:
ξ = {30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41}
P = {31, 33, 35, 37, 39, 40}

Therefore P’ = {30, 32, 34, 36, 38, 41}.



Question 4:
Given that universal set ξ = {x : 3 < x ≤ 16, x is an integer},
Set A = {4, 11, 13, 16},
Set B = {x : x is an odd number} and
Set C = {x : x is a multiple of 3}.

The elements of the set (A υ C)’ ∩ B are

Solution:
ξ = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
A = {4, 11, 13, 16}
B = {5, 7, 9, 11, 13, 15}
C = {6, 9, 12, 15}

(A υ C)’ = {5, 6, 7, 8, 10, 14}

Therefore (A υ C)’ ∩ B = {5, 7}.