explain why the set 7,9,12 is a subset of the set 5,6,7,8,9,10,11,12
The set {7, 9, 12} is a subset of the set {5, 6, 7, 8, 9, 10, 11, 12} because all the elements in the first set are also included in the second set.
To be considered a subset, every element in the first set must also be present in the second set. In this case, each element of the set {7, 9, 12} (which are 7, 9, and 12) can be found in the set {5, 6, 7, 8, 9, 10, 11, 12}. Therefore, the set {7, 9, 12} is a subset of the set {5, 6, 7, 8, 9, 10, 11, 12}.
To determine whether the set {7, 9, 12} is a subset of the set {5, 6, 7, 8, 9, 10, 11, 12}, we need to check if every element in the first set is also present in the second set.
Step 1: Check if 7 is present in the second set {5, 6, 7, 8, 9, 10, 11, 12}. Since 7 is present, we move to the next element.
Step 2: Check if 9 is present in the second set {5, 6, 7, 8, 9, 10, 11, 12}. Since 9 is present, we move to the next and final element.
Step 3: Check if 12 is present in the second set {5, 6, 7, 8, 9, 10, 11, 12}. Since 12 is present, we have checked all the elements in the first set.
Since all the elements in the first set {7, 9, 12} are present in the second set {5, 6, 7, 8, 9, 10, 11, 12}, we can conclude that the set {7, 9, 12} is indeed a subset of the set {5, 6, 7, 8, 9, 10, 11, 12}.