Sets | Class 11 chapter 1 sets | part 5 | set theory | infinix classes | maths sets | cbse

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Sets | Class 11 chapter 1 sets | part 5 | set theory | infinix classes | maths sets | cbse #sets

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Questions covered in this part :

Q) X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements
and Y has 32 elements, how many elements does X ∩ Y have ?

Q) In a school there are 20 teachers who teach mathematics or physics. Of
these, 12 teach mathematics and 4 teach both physics and mathematics.
How many teach physics ?


Q) In a survey of 400 students in a school, 100 were listed as taking apple
juice, 150 as taking orange juice and 75 were listed as taking both apple as
well as orange juice. Find how many students were taking neither apple juice
nor orange juice


Q) There are 200 individuals with a skin disorder, 120 had been exposed to the
chemical C1, 50 to chemical C2, and 30 to both the chemicals C1 and C2.
Find the number of individuals exposed to
(i) Chemical C1 but not chemical C2
(ii) Chemical C2 but not chemical C1
(iii) Chemical C1 or chemical C2


Q) In a group of 65 people, 40 like cricket, 10 like both cricket and tennis.
How many like tennis only and not cricket? How many like tennis?


Q) In a group of 70 people, 37 like coffee, 52 like tea and each person likes at
least one of the two drinks. How many people like both coffee and tea?

Set Theory is a branch of mathematical logic where we learn sets and their properties. A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a group of players in a cricket team is a set.

Since the number of players in a cricket team could be only 11 at a time, thus we can say, this set is a finite set. Another example of a finite set is a set of English vowels. But there are many sets that have infinite members such as a set of natural numbers, a set of whole numbers, set of real numbers, set of imaginary numbers, etc.


Definition of Sets

As we have already learned in the introduction, set is a well-defined collection of objects or people. Sets can be related to many real-life examples, such as the number of rivers in India, number of colours in a rainbow, etc.

Example

To understand sets, consider a practical scenario. While going to school from home, Nivy decided to note down the names of restaurants which come in between. The list of the restaurants, in the order they came, was:


The above-mentioned list is a collection of objects. Also, it is well-defined. By well-defined, it is meant that anyone should be able to tell whether the object belongs to the particular collection or not. E. g. a stationary shop can’t come in the category of the restaurants. If the collection of objects is well-defined, it is known as a set.


Types of Sets

The sets are further categorised into different types, based on elements or types of elements. These different types of sets in basic set theory are:

Finite set: The number of elements is finite
Infinite set: The number of elements are infinite
Empty set: It has no elements
Singleton set: It has one only element
Equal set: Two sets are equal if they have same elements
Equivalent set: Two sets are equivalent if they have same number of elements
Power set: A set of every possible subset.
Universal set: Any set that contains all the sets under consideration.
Subset: When all the elements of set A belong to set B, then A is subset of B