Sets and Logic

*To determine the number of subsets, count the number of elements in the set. That number is the exponent in the equation 2^X. In example {A} there are 4 colors(2^4=16). Therefore, there are 16 subsets of set {A}.

*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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