what are the subsets of A={a,b,c}
Answers
AnswEr:-
Given:-
- A set A = {a,b,c}
To Find:-
- The subsets of A.
Concept Used:-
- A subset is a set which contains the all or some elements of another set.
- For example:- There is a set X = {a,c} then Y = {a} is a subset of X as it contains the elements of set X.
So Here,
• Given set is A = {a, b, c}.
Therefore the subsets of A are as follows:-
- B = {a, b, c}.
- C = {a}.
- D = {b}.
- E = {c}.
- F = {a,b}.
- G = {b,c}.
- H = {a,c}.
- I = {}.
(Note:- Here I = {} is an emty set also a emty set is subset of all the sets.)
Therefore all sets which are mentioned above i.e. B, C, D, E, F, G, H, I are the subsets of the set A = {a, b, c}.
We can also find out how many subsets are for a single set by using a formula:-
=》 Number of subsets of a single set,
= 2 to the power m.
Where m are the number of elements in the set.
We can also verify the above formula:-
As in the question there are 3 elements in the set A.
Therefore the number of subset must be,
= 2 to the power 3.
= 2 × 2 × 2.
= 8.
Also we had found 8 subsets of the set A.
Hence the formula is also verified.
Answer:
Subset of A= {} , {a} ,{b} ,{c} ,{a,b} ,{a,c}, {b,c}
Step-by-step explanation:
There are 8 subset of A, and all of them except A itself considered proper subset.
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