NCERT Class 11-Math's Exemplar Chapter 1 Sets CBSE Board Problems

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Intersection of sets:

The intersection of two sets A and B is the set which consists of all those elements which belong to both A and B. Symbolically, we write.

When , then A and B are called disjoint sets.

Fig-1.3-(a)-Intersection of sets

Intersection of Sets

Fig-1.3-(b)-Intersection of sets

Intersection of Sets

Some properties of the operation of intersection

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Difference of sets The difference of two sets A and B, denoted by A – B is defined as set of elements which belong to A but not to B. We write

also,

Complement of a set:

Let U be the universal set and A a subset of U. Then the complement of A is the set of all elements of U which are not the elements of A. Symbolically, we write

Some properties of complement of sets

(i) Law of complements:

(a)

(b)

(ii) De Morgan’s law

(a)

(b)

(iii)

(iv)

Formulae to solve practical problems on union and intersection of two sets

Let A, B and C be any finite sets. Then

(a)

(b) If

(c)

Solved Examples

Short Answer Type

Question 1:

Write the following sets in the roaster form.

(i) is a positive integer less than and is an odd number}

(ii)

Answer:

(i) is always an odd number for all positive integral values of . In particular, is an odd number for . Thus, .

(ii)

Thus,

Question 2:

State which of the following statements are true and which are false. Justify your answer.

(i)

(ii)

(iii)

Answer:

(i) False

Since, 37 has exactly two positive factors, 1 and 37, 37 belongs to the set.

(ii) True

Since, the sum of positive factors of 28

(iii) False

is not a multiple of .

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