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Online Quiz (Worksheet A B C D)

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Grade 8 - Mathematics
4.48 Sets Review

In Mathematics, a well-defined collection of definite objects is called a set.

*Is a collection of unique elements.
*It is important that the such a collection is well defined. If there is any ambiguity, the collection is not a set.
*George Cantor is regarded as the "Father of Set theory".
*The concept of "Sets" is basic in all branches of mathematics.
*It has proved to be of particular importance in the foundations of relations and functions, sequences, geometry, probability theory etc.
*The study of sets has many applications in logic, philosophy, etc.

Sets Notation:
*It is indicated by list of its elements enclosed in {}.
*It can be given names such as: A B C D F .............etc
Natural numbers less than 10 can be written in set notation as N = {1,2,3,4,5,6,7,8,9}
A collection of "red sports cars" is a set.
A collection of "good sports car" is not a set, since what is good for one person may not be good for someone else.
* Let D represent the set of days of the week.
Then D = {Sunday, Monday, Tuesday, Wednusday, Thursday, Friday, Saturday}
We can use belong to symbol to indicate that something is in the set.
Monday D and is read as: Monday is a member of the set D
But Holiday D is read as Holyday is not a member of the set D

Representation of Sets:
There are two methods of representing a set.
(i) Roster Method
(ii) Set builder form
Two special sets:
Empty set or Null set or {}
A set which has no elements is called an empty set.
Universal set represents U
A set which has all the elements in the universe of discourse is called a universal set

Other sets:
Subset: A set A is a subset of a set B if and only if everything in A is also in B. In other words, a subset is a portion of a set. It is denoted by or
Superset: A superset is a set that includes other sets. It is denoted by or
A = {1,2,3} and B = {1,2,3,4,5,6,7,8}. Here A is a subset of B and B is superset of A.
A B then B A
Finite and Infinite Sets
A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set.
Examples :
Finite set: Set of all natural numbers less than 5.
Infinite set: Set of all natural numbers.

Directions: Solve the following using set.
Q 1: Which of the following is not a well defined set?
Good days in a week
Days of the week
Days of the week starting with a 'p'
Days of the week starting with a 's'

Q 2: Two sets are equal if and only if they have the same elements. Example: A = {1,2,3} and B = {1,2,3}

Q 3: Set is a collection of unique elements.

Q 4: Which set do the following numbers: 66, -4, 0, 55, 98 belong to?
Whole numbers
Natural numbers

Q 5: Each element is a member of the set (or belongs to the set).

Q 6: The null set is a subset of every set.

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!

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