Let U = {u, n, i, t, e} FIND THE SUBSETS

To find all the subsets of a given set, you can use the concept of power set. The power set of a set is the collection of all possible subsets of that set, including the empty set and the set itself.

For the set U = {u, n, i, t, e}, let's find its power set.

Step 1: Determine the total number of elements in the power set. Since U has 5 elements, the power set will have 2^5 (2 to the power of 5) elements. In this case, it will have 32 elements.

Step 2: Enumerate all the possible binary combinations from 0 to 31. Since there are 32 elements in the power set, you will have 32 combinations in binary format.

Step 3: For each binary combination, map the elements of U accordingly. Consider each bit of the binary number as an indicator for including or excluding the corresponding element from U. For example, if the binary number is 01011, it means the subset will include the second, fourth, and fifth elements from U.

Step 4: Repeat Step 3 for all 32 binary combinations to obtain all the subsets. Keep in mind that the binary combinations with all '0's represent the empty set, and the binary combinations with all '1's represent the set U itself.

Here are all the subsets of the set U = {u, n, i, t, e}:
{} (empty set)
{u}, {n}, {i}, {t}, {e}
{u, n}, {u, i}, {u, t}, {u, e}, {n, i}, {n, t}, {n, e}, {i, t}, {i, e}, {t, e}
{u, n, i}, {u, n, t}, {u, n, e}, {u, i, t}, {u, i, e}, {u, t, e}, {n, i, t}, {n, i, e}, {n, t, e}, {i, t, e}
{u, n, i, t}, {u, n, i, e}, {u, n, t, e}, {u, i, t, e}, {n, i, t, e}
{u, n, i, t, e} (set U itself)

So, the subsets of U are: {}, {u}, {n}, {i}, {t}, {e}, {u, n}, {u, i}, {u, t}, {u, e}, {n, i}, {n, t}, {n, e}, {i, t}, {i, e}, {t, e}, {u, n, i}, {u, n, t}, {u, n, e}, {u, i, t}, {u, i, e}, {u, t, e}, {n, i, t}, {n, i, e}, {n, t, e}, {i, t, e}, {u, n, i, t}, {u, n, i, e}, {u, n, t, e}, {u, i, t, e}, {n, i, t, e}, {u, n, i, t, e}.