Question

Suppose A = {a,b,c,d}. How many subsets of 2 elements are possible?

Answer 1

Answer:

6

Step-by-step explanation:

possible subsets with 2 elements are

{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}

Answer 2

SOLUTION

GIVEN

A = {a,b,c,d}.

TO DETERMINE

The number subsets of 2 elements

CONCEPT TO BE IMPLEMENTED

Set :

A set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

Subset :

A set S is said to be a subset of T if every element of S is an element of T . It is written as S ⊆ T

EVALUATION

Here the given set is

A = {a,b,c,d}.

Number of elements in A = 4

We have to find the number subsets of 2 elements

Hence the required number of subsets

$\sf{ = {}^{4}C_2 }$

$\sf{ = \dfrac{4!}{2! \: (4 - 2)!} }$

$\sf{ = \dfrac{4!}{2! \: 2!} }$

$\sf{ = \dfrac{ 4 \times 3 \times 2!}{2! \: 2!} }$

$\sf{ = \dfrac{4 \times 3 }{2! } }$

$\sf{ = \dfrac{12 }{2} }$

= 6

More precisely the subsets are

{a,b},{a,c},{a,d},{b,c},{b,d},{c,d}

FINAL ANSWER

Hence the required number of subsets = 6

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