Question

List all the possible subsets of Set H = { 4,3,6,5}

Answer 1

Given Set H:

$H=\lbrace4,3,6,5\rbrace$

You can find the number of subsets the set has by using this formula:

$Number\text{ }of\text{ }subsets=2^n$

Where "n" is the number of elements the set has.

In this case:

$n=4$

Then:

$Number\text{ }of\text{ }subsets=2^4=16$

By definition, given a set:

$\lbrace a,b\rbrace$

Its subsets are:

$\lbrace a\rbrace,\lbrace b\rbrace,\lbrace\phi\rbrace,\lbrace a,b\rbrace$

Therefore, in this case, you can determine that the possible subsets of the given set are:

$\lbrace4\rbrace,\lbrace3\rbrace,\lbrace6\rbrace,\lbrace5\rbrace,\lbrace4,3\rbrace,\lbrace4,6\rbrace,\lbrace4,5\rbrace,\lbrace3,6\rbrace,\lbrace3,5\rbrace,\lbrace6,5\rbrace,\lbrace4,3,6\rbrace,\lbrace3,6,5\rbrace,\lbrace4,6,5\rbrace,\lbrace4,3,5\rbrace,\lbrace4,3,6,5\rbrace,\lbrace\phi\rbrace$

Hence, the answer is:

$\lbrace4\rbrace,\lbrace3\rbrace,\lbrace6\rbrace,\lbrace5\rbrace,\lbrace4,3\rbrace,\lbrace4,6\rbrace,\lbrace4,5\rbrace,\lbrace3,6\rbrace,\lbrace3,5\rbrace,\lbrace6,5\rbrace,\lbrace4,3,6\rbrace,\lbrace3,6,5\rbrace,\lbrace4,6,5\rbrace,\lbrace4,3,5\rbrace,\lbrace4,3,6,5\rbrace,\lbrace\phi\rbrace$