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Subsets of {s, t}

# Subsets of {s, t}

by Breiann
(Florida)

What is the sub set of {s, t}?

Identify the improper subset and all proper subsets.

Can elements be listed more than once?

Can elements be listed in any order?

### Comments for Subsets of {s, t}

 Oct 09, 2012 Subsets by: Staff Answer: A subset contains at least one of the elements the set. For example, { s } and { s, t } are both subsets of {s, t}. IMPROPER SUBSET: An improper subset contains ALL the elements of the set. {s, t} is the improper subset of {s, t}. PROPER SUBSET: A proper subset contains one or more of the elements the set, but not all the elements. For example, { c } and { t } are proper subsets of {s, t}. ELEMENTS in a set or subset CAN BE LISTED MORE THAN ONCE without changing the set or subset. For example, {s,s,s} and {t,t,t} are still proper subsets of {s, t}. ELEMENTS in a set or subset CAN BE LISTED IN ANY ORDER without changing the set or subset. For example, {s, t} and {t, s} are the same set, even though the elements are not listed in the same order. ------------------------------------ Subsets of {s, t} The following calculations do not include the “null set” (the empty set), Ø = {}. Improper Subset = 1: {s, t} Proper Subsets = (see calculations below): To find the number of proper subsets, you must determine how many COMBINATIONS (not permutations) of the elements s, and t are possible when you select 1 element (you cannot select both elements because that would be an improper subset, which you have already accounted for). There is a formula which you can use to calculate these combinations (again, not permutations, but combinations): C(n,r) = n! / r! (n - r)! 0 ≤ r ≤ n. n = number of elements in the set {s, t} = 2 r = number of elements selected = 1 [r = 2 will not be used since that is the improper subset. It has already been accounted for.] Order is not important Repetition is not allowed Selecting any 1 element from the 2 possible choices n = number of elements = 2 r = number of elements selected = 1 C(n,r) = n! / r! (n - r)! C(2,1) = 2! / 1! (2 - 1)! C(2,1) = (2*1) / 1*1 C(2,1) = 2 / 1 C(2,1) = 2 The proper subsets when 1 element is selected are: {s} {t} The number of all possible subsets of {s, t} = 3 These are: Proper Subsets: {s} {t} Improper Subset: {s, t} (This DOES NOT include the “null set”, Ø = {}. If you wish to include the null set, the final answer is 3 + 1 = 4, or 2². 2² = 2ⁿ where n = 2 ) Thanks for writing. Staff www.solving-math-problems.com