Let the Universal Set, S, have 136 elements. A and B are subsets of S. Set A contains 34 elements and Set B contains 98 elements. If Sets A and B have 22 elements in common, how many elements are in A but not in B?
34-22
If the universal set is given by S={11,22,33,44,55,66},and A={11,22}, B={22,44,55}, C={11,55,66} are three subsets, Find the following sets:
a-(A∪B) ̅
To find out how many elements are in set A but not in set B, you can subtract the number of elements in the intersection of A and B from the total number of elements in A.
1. Find the number of elements in A: 34
2. Find the number of elements in the intersection of A and B: 22
3. Subtract the number of elements in the intersection from the number of elements in A: 34 - 22 = 12
Therefore, there are 12 elements in set A but not in set B.
To find out how many elements are in set A but not in set B, we need to consider the number of elements in set A and subtract the number of elements that are in both sets A and B.
Given that set A contains 34 elements and set B contains 98 elements, and there are 22 elements common to both sets, we can use the formula for finding the number of elements in the union of two sets:
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A ∪ B| represents the number of elements in the union of sets A and B, |A| represents the number of elements in set A, |B| represents the number of elements in set B, and |A ∩ B| represents the number of elements in the intersection of sets A and B.
So, substituting the given values:
|A ∪ B| = 34 + 98 - 22
= 112
Now, we need to find the number of elements in set A that are not in set B, which can be calculated by subtracting the number of elements in the intersection of sets A and B from the number of elements in set A:
|A - B| = |A| - |A ∩ B|
Substituting the given values:
|A - B| = 34 - 22
= 12
Therefore, there are 12 elements in set A that are not in set B.