How to Find Complement of a Set | Universal Set | MathOGuide

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How to Find Complement of a Set | Universal Set | MathOGuide

To find the complement of a set within a universal set, subtract the elements of the set you want to find the complement of from the elements of the universal set. The complement consists of all elements in the universal set that are not in the given set.


Let's break it down:

1. **Universal Set**: This is the set that contains all the elements under consideration. It's like the "big picture" set.

2. **Given Set**: This is the set for which you want to find the complement. It's a subset of the universal set.

3. **Complement**: The complement of a set consists of all the elements that are in the universal set but not in the given set.

Here's how you find it:

1. Identify the universal set and the given set.
2. Subtract the given set from the universal set.
3. The result is the complement of the given set within the universal set.

Let's say we have a universal set
U = {1, 2, 3, 4, 5})and
a given set
A = {2, 4}

To find the complement of set A within the universal set U

1. Identify the universal set
U = {1, 2, 3, 4, 5} and
the given set
A = {2, 4}
2. Subtract the elements of set A from the elements of set U

U minus A = {1, 3, 5}

So, the complement of set A within the universal set U
is{1, 3, 5}.
These are the elements of U that are not in A .
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