Sets - ANS ✓- Groups of values that have some common property, such as the
negative odd integers greater than -10 or all positive integers that are evenly
divisible by 3.
- The items in sets are called elements or members.
- Finite Set
- Infinite Set
- Empty Set
Finite Set - ANS ✓- If all the elements in a set can be counted, such as "the
number of species of birds in North America," that set is finite.
Infinite Set - ANS ✓If the elements in a set are limitless, "all positive numbers
that are evenly divisible by 3," that set is infinite.
Empty Set - ANS ✓- A set with no elements.
- Represented by the symbol 0 with a slash through it.
Lists - ANS ✓- Similar to a finite set except that the order of the elements matters
and that duplicate members can be included.
- So, 1,2,3 and 3,2,1 are different lists, and 1, 2, 3, 2 is a valid list.
- Order DOES matter.
- Because order matters, elements can be uniquely identified by their position,
such as "first element" or "fifth element"
- Notice that sets are usually enclosed by { and }, and lists are NOT.
QUANTITATIVE REA
, 2
QUAN
Set Operations - ANS ✓- The INTERSECTION of two sets is a set that consists of
all the elements that are contained in both sets (an overlap between the sets).
- Th intersection of two sets is labeled as A (Upside down U) B.
- The UNION of two sets is the set of all the elements that are elements of either
or both sets and is written A U B.
- If sets have no common elements, there are referred to as mutually exclusive,
and their intersection is the empty set.
Venn Diagrams - ANS ✓- A helpful way to analyze the relationship among sets.
- The set of all possible elements that have the characteristics of the sets
represented by the circles in this diagram is called a Universal Set and is
represented by U.
Inclusion-Exclusion Principle - ANS ✓- A basic counting principle for sets.
- To find the number of elements in the union of two sets, use this formula: |A U
B| = |A| + |B| - |A (upside down u) B|.
- This formula adjusts for the double counting of elements that are in both sets.
Multiplication Principle - ANS ✓- When choices or events occur one after the
other and the choices or events are independent of one another, the total number
of possibilities is the product of the number of options for each.
- Occasionally a GRE question may require a careful analysis of the number of
options for each choice.
- In situations where choices are "or" rather than "and," as long as the two groups
are mutually exclusive, add instead of multiplying.
reason - ANS ✓clear and ordered thinking
quantitatively - ANS ✓of, concerning, or capable of being measured or
expressed as a quantity
QUANTITATIVE REA
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