NULL SET AND SINGLETON SET

Solved Questions

Question 1 :

Identify the following sets as null set or singleton set.

(i) A = {x : x ∈N, 1 < x < 2}

Solution :

N is the natural number and it should be grater than 1 and lesser than 2. Since it is not possible, the set A will not contain any elements. It is null set.

(ii) B = The set of all even natural numbers which are not divisible by 2

Solution :

Even number means, a number which is divisible by 2. But the set B will contain the elements which are not divisible by 2. It is not possible. It is null or empty set.

(iii) C = {0}.

Solution :

The set C contains only one element. Hence it is singleton set.

(iv) D = The set of all triangles having four sides.

Solution :

All triangles will have only three sides. Hence D is empty set.

Question 2 :

If S = {square, rectangle, circle, rhombus, triangle}, list  the elements of the following subset of S.

(i) The set of shapes which has 4 equal sides.

Solution :

Let A be the set, which contains the shape of 4 equal sides.

A  =  {Square, Rhombus}

(ii) The set of shapes which has no sides.

Let B be the set, which contains the shape which have no sides.

B  =  {Circle} 

(iii) The set of shapes in which the sum of all interior angles is 180^o

Solution :

For any triangle the sum of all interior angles is 180, hence

C  =  {Triangle}

(iv) The set of shapes which have 5 sides.

Solution :

In the given set no shape will contain 5 sides. Hence it is a empty set.

Question 3 :

If A = {a, {a, b}}, write all the subsets of A.

Solution :

Subset of A  =  {{ }, {a}, {a, b}, {a, {a, b}}}

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