MUlti-Criteria Grouping - Select A Fruit

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 6 - 63 **

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Multi-Criteria Grouping - Select A Fruit

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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**:

S_{7}P_{6}A_{63} (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.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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