With 5 elements in A={20,1,6,10,11}, there are 2^5=32 possible subsets, including the null set, and A itself. Any subset that is identical to A is NOT a proper subset. Therefore there are 31 proper subsets, plus the subset {20,1,6,10,11}.
The subsets are: null set {} (has no elements) ........total 1 {20},{1},{6},{10},{11}.......................total 5 {20,1},{20,6}...{10,11}.....................total 10 {20,1,6},{20,1,10},...{6,10,11}.........total 10 {20,1,6,10}...{1,6,10,11}.................total 5 {20,1,6,10,11}.................................total 1 Altogether 32 subsets.
Couple of ways to solve this. Here is one method Convert all times to minutes and find the total number of minutes they spent on all 3 activities. Then convert to hours and minutes and subtract from the end time of 5;28 to get the start time of all activities which is also the start time of watching the movie (first activity)
Total time spent = 138 + 34 + 72 = 244 minutes = 4 hours and 04 minutes
Subtract 4:04 from 5:28 to get 1:24pm
Check Movie watch starts at 4:04, ends at 1:24 + 2:18 or 3:42pm Card game starts at 3:42pm ends at 3:42+0:34 ==> 4:16pm Soccer starts at 4:16pm ends at 4:16pm + 1:12 ==> 5;28pm
