A computer is printing out subsets of a 3 element set (possibly including the empty set).1) How many different subsets are there?12) At least how many sets must be printed to be sure of having at least 2 identical subsets on the list?3) At least how many identical subsets are printed if there are 25 subsets on the list?

Given: A computer is printing out subsets of a 3 element set (possibly including the empty set). From the above data, we have to find the following lists. 1) How many different subsets are there?2) At least how many sets must be printed to be sure of having at least 2 identical subsets on the list?3) At least how many identical subsets are printed if there are 25 subsets on the list?1) How many different subsets are there? Explanation: Total number of possible subsets of 3 element sets including empty set are: = 23= 8 Hence, different subsets are 8.2) At least how many sets must be printed to be sure of having at least 2 identical subsets on the list? Explanation: Sets that must be printed to be sure of having at least 2 identical subsets on the list are: = (23 × 1) + 1= 9 Hence, sets having at least 2 identical subsets on the list are 9.3) At least how many identical subsets are printed if there are 25 subsets on the list? Explanation: Identical subsets that are printed if there are 25 subsets on the list are: 25 = 23 × 3 + 1 Thus, 3 + 1 = 4 Hence, 4 identical subsets are printed.