Question

write the cardinal numbers of each of the following sets​

Answer 1

To Find :

The cardinal Number of the given sets:

$\displaystyle \rm i)a = \{x :x \in n \: and \: x \leqslant 6 \}$

$\displaystyle \rm \: ii)b = \{set \: of \: all \: letters \: in \: word \: india \}$

$\displaystyle \rm iii)c = \{set \: of \: prime \: number \: between \: 6 \: and \: 16 \}$

What is Cardinal Number?

Cardinal Number is the total number of elements in a set.

For eg,

A = {1,2,3}

So, Cardinal number of A is given by:

n(A) = 3

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Solution :

1] Given the set :

$\displaystyle \rm i)a = \{x :x \in n \: and \: x \leqslant 6 \}$

This set says that, A contains those elements which are Natural number equal or less than 6.

As we know, the numbers can be :

• 1,2,3,4,5 and 6

So, We get that :

A = {1,2,3,4,5,6}

Hence, :

• n(A) = 6

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2] Given the set :

B = set of all the word in 'INDIA'

Now this set says that the set B contains all the letters in the word INDIA, so the letters are :

• I
• N
• D
• I
• A

So, The set B :

• B ={I,N,D,I,A}
• n(B) = 5

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3] Given The set :

C = set of prime numbers between 6 and 16,

So, this set says that the set C contains all the prime numbers between 6 and 16, so the numbers are :

• 7,11,13

Hence, C={7,11,13}

• n(C) = 3