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Statistics & Probability-3

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Pupil
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(Virtual university of Pakistan)
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Date Posted: 5/11/2008 5:06:56 AM  Status: Live
Statistics & Probability-3
Course Textbook Chapter Problem
Statistics and Probability Statistics (4th) by Freedman, Pisani, Purves N/A N/A
Question Details:

Define Set and its properties. Also explain the Venn diagram.


Ahm3d™

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Date Posted: 5/11/2008 10:45:17 AM  Status: Live
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Response:

set

By a "set" we mean any collection M into a whole of definite, distinct objects m (which are called the "elements" of M) of our perception [Anschauung] or of our thought.

The elements of a set, also called its members, can be anything: numbers, people, letters of the alphabet, other sets, and so on. Sets are conventionally denoted with capital letters. The statement that sets A and B are equal means that they have precisely the same members (i.e., every member of A is also a member of B and vice versa).

Unlike a multiset, every element of a set must be unique; no two members may be identical. All set operations preserve the property that each element of the set is unique. The order in which the elements of a set are listed is irrelevant, unlike a sequence or tuple.

venn diagram:
Sets A and B
Sets A and B

The following example involves two sets, A and B, represented here as coloured circles. The orange circle, set A, represents all living creatures that are two-legged. The blue circle, set B, represents the living creatures that can fly. Each separate type of creature can be imagined as a point somewhere in the diagram. Living creatures that both can fly and have two legs — for example, parrots — are then in both sets, so they correspond to points in the area where the blue and orange circles overlap. That area contains all such and only such living creatures.

Humans and penguins are bipedal, and so are then in the orange circle, but since they cannot fly they appear in the left part of the orange circle, where it does not overlap with the blue circle. Mosquitoes have six legs, and fly, so the point for mosquitoes is in the part of the blue circle that does not overlap with the orange one. Creatures that are not two-legged and cannot fly (for example, whales and spiders) would all be represented by points outside both circles.

The combined area of sets A and B is called the union of A and B, denoted by A ∪ B. The union in this case contains all things that either have two legs, or that fly, or both.

The area in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B. For the example, the intersection of the two sets is not empty, because there are points representing creatures that are in both the orange and blue circles.

Sometimes a rectangle called the "Universal set" is drawn around the Venn diagram to show the space of all possible things. As mentioned above, a whale would be represented by a point that is not in the union, but is in the Universe (of living creatures, or of all things, depending on how one chose to define the Universe for a particular diagram).

[edit]

r3dd's Comment:
thnX u so Much...!!!





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