Select A Fruit Container A, contains 7 apples. Container B, contains 7 peaches. You are asked to select a fruit from each of the following spaces formed by containers A and B:
(a) A ∪ (A ∩ B)
(b) A ∩ (A ∪ B)
(c) (A - B) ∪ B
What is the maximum number of apples you can select? What is the maximum number of peaches you can select?
Hint: simplify expressions before selecting. A ∪ B (fig. 7.87a) means the set of elements in A or in B or in both (if in both, counted only once). A ∩ B ( fig. 7.87b) means the set of elements in A and in B (elements common to both A and B). A - B (fig. 7.87c) means the set of elements in A but not in B.

The string:
S7P6A63 (Multi-Criteria Combination).
The math: Pj Problem of Interest is of type Grouping. There are two groups of fruits (apples and peaches) from which to select. So this is a problem of type multi-criteria grouping.
(a) A ∪ (A ∩ B) = A. This is because there is no element common to both A and B.
So, A ∩ B = 0 and A ∪0 = A.
So, only apples will be selected because the space does not include peaches.
So, maximum number of apples you can select is 7.

(b) A ∩ (A ∪ B) = A. This is because A is the common space.
So, maximum number of apples you can select is 7. No peaches to be selected.

(c) (A - B) ∪ B = A ∪ B.
So, maximum number of apples you can select is 7 and maximum number of peaches you can select is also 7.

Math

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