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What is an improper subset?
An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.
What subset is?
For example, if we have a set of numbers called A which has 3 members(in our case numbers): A={2,5,6} this set has 8 subsets (2^3) which are as follow: the empty set: ∅ {2},{5},{6} {2,5},{2,6},{5,6} {2,5,6}
How many subsets are in the set 12345?
Number of subsets with no members = 1Number of subsets with one member = 5.Number of subsets with 2 members = (5 x 4)/2 = 10.Number of subsets with 3 members = (5 x 4 x 3 /(3 x 2) = 10.Number of subsets with 4 members = (5 x 4 x 3 x 2)/(4 x 3 x 2) = 5.Number of subsets with 5 members = 1Total subsets = 1 + 5 + 10 + 10 + 5 + 1= 32.A set with n elements has 2n subsets. In this case n = 5 and 25 = 32.The proof in the case that n = 5 uses a basic counting technique which say that if you have five things to do, multiply together the number of ways to do each step to get the total number of ways all 5 steps can be completed.In this case you want to make a subset of {1,2,3,4,5} and the five steps consist of deciding for each of the 5 numbers whether or not to put it in the subset. At each step you have two choices: put it in or leave it out.
What is the possible no of reflexive relations on a set of 5 elements?
The total no. of reflexive relations on a set A having n elements is 2^n(n-1).Thus, the required no. is 2^20 = 1 048 576
What is the cardinal number of a set?
The cardinal number of a set is the number of elements in the set. Example: the cardinal number of the set {6, prune, 675, biscuit, London} is 5, since the set contains five elements. If a set contains repeated elements, they should only be counted once. Example: the cardinal number of the set {6, 7, 3, 4, 4, 7} is 4 (not 6) since the fours and sevens are only counted once.
