Suppose Set B contains 69 elements and the total number elements in either Set A or Set B is 107. If the Sets A and B have 13 elements in common, how many elements are contained in set A?

Sets A and B have 13 elements in common. The total of their union is 107. But this 107 only accounts once for the 13 elements in common. Thus, the two sets actually possess a total of 107 + 13 = 120 elements between them. Finally, 120 - 69 = 51. The number of elements in set B is 51.

QED.

To find the number of elements in set A, we need to understand the relationship between the elements in set A, set B, and the common elements.

Let's start by considering the total number of elements in either set A or set B. We are given that this total is 107. Mathematically, we can represent this as:

|Set A ∪ Set B| = 107

Next, we know that set B contains 69 elements. Mathematically, we can represent this as:

|Set B| = 69

We are also given that there are 13 elements common to both set A and set B. Mathematically, we can represent this as:

|Set A ∩ Set B| = 13

To find the number of elements in set A, we need to find |Set A|. We can do this by rearranging the equation |Set A ∪ Set B| = 107.

|Set A ∪ Set B| = |Set A| + |Set B| - |Set A ∩ Set B|

Substituting the known values, we have:

107 = |Set A| + 69 - 13

Simplifying the equation by combining like terms, we get:

107 = |Set A| + 56

To isolate |Set A|, we subtract 56 from both sides of the equation:

107 - 56 = |Set A|

Finally, calculating the equation, we find:

|Set A| = 51

Therefore, set A contains 51 elements.