Question

State which of the following sets are finite and which are infinite. Give reasons for your answer.
(i) A = {x : x ∈ N and x < 100} (ii) B = {x : x ∈ N and x < 5}
(iii) C = {1², 2², 3², …..} (iv) D = {1, 2, 3, 4}
(v) {x : x is a day of the week}.

Answer 1

1. finite set

2. finite set

3. infinite set

4. infinite set

5. finite set

Answer 2

Answer:

Step-by-step explanation:

A set where the count of elements comes to an end is called a finite set and a set that is not finite is called an Infinite set,

1 ) A = { x : x ∈ N and x < 100 }

A = { 1 , 2 , 3 , ....., 98 , 99 }, thus

Thus, A is a finite set .

2) B = { x : x ∈ N and x < 5 }

B = { 1 , 2 , 3 , 4 }

Thus, B is finite set .

3) C = { 1² , 2² ,3² , .... }

It is an infinite set

4) D = { 1 , 2 , 3 , 4 }

It is a finite Set .

5) E = { x : x is a day of the week }

The days of the week can be Monday , Tuesday , Wednesday, Thursday , Friday , Saturday and Sunday

Thus, E is finite set .