Finite, infinite sets, subsets

A finite set is a set whose members are countable. Examples of finite sets are:

1. K = {1, 3, 5, 7, 11}
2. C = {Students in Aboodo High School}

An infinite set is a set whose members are uncountable. Examples of infinite sets are:

1. A = {1, 2, 3, 4 …}
2. B = {Even numbers}

Suppose
A = {1, 3, 5, 7, 9, 11} and
B = {1, 5, 9}

We may say that B is a subset of A since all the members of set B are also members of set A. In symbols, we would express the relationship like this: B⊂A (read B is a subset of A) or A⊃B (read A is a superset of B).

To find all the subsets of a set, note that the empty or null set, { } or Ø, is a subset of any set.

Also note that any set is a subset of itself.

Question: Find all the subsets of set Y = {3, 5, 7}.

Answer:
The subsets of set Y = {3, 5, 7} are:
Ø, {3}, {5}, {7}, {3, 5}, {3, 7}, {5, 7}, {3, 5, 7}

When discussing sets, it’s useful to assume that all the sets under consideration are subsets of a well-defined set – the universal set.


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