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If ‘A’ is the set of composite numbers less than 9. Then list all the subsets of ‘A’.

Last updated date: 17th Jun 2024
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Hint: Try to recall the definition of composite numbers and form the set A. Once you have set A you can easily form its subsets. Remember that set A will only contain those composite numbers which are less than 9, i.e., 4, 6 and 8.

Complete step by step answer:
Before moving to the solution, let us talk about the definitions of Prime numbers. The numbers which are divisible by 1 and the number itself, and has no other factors are called primes. For example: 3, 5 etc.
Now, let us move to the definition of composite numbers. The positive integers which are divisible by more than 2 numbers, i.e., the positive integers which are not primes are composite numbers. For example: 4, 6, 9 etc.
Now let us move to the solution to the above question. Let us first find out the elements of set A.
According to the definition of composite numbers and the constraint that elements are less than 9, we can say that the elements are 4, 6 and 8. So, set A = {4,6,8}.
Now let us move on to find the subsets of A. The subsets of A are:
$\phi ,\{4\},\{6\},\{8\},\{4,6\},\{6,8\},\{4,8\},\{4,6,8\}$

Note: Be careful about what is asked in the question. As the non-empty subsets, subsets and proper subsets are three different quantities and have different answers for a given set. Also, remember that the number of subsets of a set containing n elements is given by ${{2}^{n}}$ , which can be used to check whether you have missed some subsets or not.