*In the list of subsets, the NULL SET is ALWAYS included. You can write the null set with empty bracets, {}, or as Ø.
* The notation for an element of a set is :
* The notation for when it is not an element of a set is :
* The notation for a subset is :
* EVERY SUBSET IS A SUBSET OF ITSELF!!! |
Proper Subsets:
If a set is a subset of a different set but is not the exact same set, then it is called a proper subset.
*The notation of a proper subset is:
*The notation when it is not a proper subset is:
To express the number of elements in a set we write: n(A)."n" is for "number" and "(A)" describes the set in question.
A "Finite" set has a countable number of elements. An "Infinite" set has an uncountable number of elements. For example:
N={natural numbers}
Z={integers}
R={real numbers}
Q={rational numbers}
Intersection:
When two different sets share common elements, it is called an intersection. We write this as "", meaning intersection of. For example:
A_B= A "intersection" B
A={1,2,3,4}
B={2,4,6,8}
A_B={2,4}
Union:
A union combines the elements of two sets. We write this as "U". For example:
A U B = A "union" B
A={1,2,3,4}
B={2,4}
A U B = {1,2,3,4}
* The equation for the number of elements in a union is: n(AUB)=n(A)+n(B)-n(A_B)
* To express a specific set we use set builder notation. It is a format or template to describe the set in which to analyze, solve, etc.
{x|xEN, 6< x < 12}
The first "x" represents the variable. The second part uses the "|" symbol which stands for "such that". The rest of the notation informs you of the conditions or requirements of the variable.
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