Question

Write the cardinal number of the following sets:

a) A = {Set of letters in the word “LOCK”}

b) B = {Prime numbers less than 6}​

Answer 1

ANSWER :

(a)

❖ Given :-

• ➻ A = {Set of letters in the word “LOCK”}

❖ To find :-

• ➻ The cardinal number of Set A.

❖ Required Answer :-

$\huge{ \bigstar \sf{ \: \: \underline{n (A) = 4} }}$

❖ Explanation :-

The letter of the word "LOCK" are : L, O, C, K

The number of letters in the word "LOCK" is : 4

• ➻ Hence, the Cardinal number of Set A is n (A) = 4.

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

(b)

❖ Given :-

• ➻ B = {Set of Prime numbers less than 6}

❖ To find :-

• ➻ The cardinal number of Set B.

❖ Required Answer :-

$\huge{ \bigstar \sf{ \: \: \underline{n (B) = 3} }}$

❖ Explantion :-

The prime numbers less than 6 are : 2, 3, 5

The number of prime numbers less than 6 is : 3

• ➻ Hence, the Cardinal number of Set B is n(B) = 3.

KNOW MORE :

❖ Set :-

• ➻ According to Cantor's concept, "A set is a collection of well defined and distinct objects". The word well defined means that given any object it must be possible to tell beyond doubt whether that object belongs to the collection or not and the word distinct means that no two elements of the set are same.

❖ Cardinal Number :-

• ➻ Cardinal Number of a finite set suppose P is the number of distinct elements of the finite set P.

• ➻ Cardinal number of a finite set suppose P is denoted as n(P).

❖ Finite Set :-

• ➻ A set containing a finite number of elements i.e., a countable number of elements such that the process of counting stops after a certain definite stage is called a Finite Set.

❖ Infinite Set :-

• ➻ A set containing unlimited number of elements i.e., uncountable number of elements is called an Infinite Set.