Question

Which of the given sets are finite or infinite:
a.The set of months of a year
b..{1, 2, 3, . . .}
c.{1, 2, 3, . . . 99, 100}
d.The set of positive mtegers greater than 100
e.The set of prime numbers less than 99

Answer 1

a. The set of months of a year. Let A is given set then we can write it A = {Jan, Feb, Mar, Apr... Dec} here you can see that set A has finite elements e.g., 12.
so, it is finite set.

b. {1, 2, 3, ......} , it is the set of all natural numbers and there is not condition of limit. so, it is infinite set.

c. {1, 2, 3, ....99, 100} , it is the set of all natural numbers less than and equal to 100. hence, it is finite set. because number of elements is finite.

d. The set of positive integers greater than 100.e.g., {101, 102, 103..... } here you can see number of elements can't be counted so, it is infinite set.

e. The set of prime number less than 99.e.g., {2,3,5,7,11, 13, 17, .... 99} here you can see the number of elements in the set can be counted so, it is finite set.

Answer 2

Answer:

a , c , e are finite ,

b , d are infinite sets

Step-by-step explanation:

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Finite and infinite set :

A set is called a finite set

if it's cordinal number is a

definite whole number.

We can say that a set is infinite

if it is not finite .

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Now ,

a ) The set of months of a year.

Number of months in a year = 12

Therefore ,

It is a finite set.

b ) { 1 , 2 , 3 , 4 ,... }

Number of elements is infinite.

Therefore ,

It is an infinite set .

c ) { 1,2,3,.....,100 }

Number of elements in the set

= 100

Therefore ,

It is a finite set .

d ) The set of positive integers

greater than 100

= { 101, 102, 103 ,.... }

Number of elements is not

finite .

Therefore ,

It is a infinite set.

e ) Set of prime numbers less

than 99.

= { 2,3,5,7,11,13,17,19,...97 }

Number of elements is

Countable ( finite )

Therefore ,

It is a finite set .

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