Question

Let A = {a, b, c, d, e}, B = {a, c, e, g}, and C = {b, e, f, g}. Then verify the following identities:

Answer 1

The question entails verifying mathematical identities for sets A, B, and C, considering the intersection and union of sets or vector operations like cross product and dot product.

Step-by-step explanation:

The question is asking to verify mathematical identities involving sets A, B, and C. The identities given seem to be a mix of vector operations and set operations which are not directly comparable. However, we can clarify that for set operations:

If we consider union and intersection as analogous to addition and multiplication, respectively, the distributive law states that for any sets A, B, and C:

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• A \u2229 (B \u222a C) = (A \u2229 B) \u222a (A \u2229 C)

Here, \u2229 is the intersection operator and \u222a is the union operator. Also, vector operations such as cross product (×) and dot product (.) have their own algebraic rules. For instance, the cross product is anticommutative, and the dot product is commutative:

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• A × B = -B × A
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• A . B = B . A

Thus, verifying each identity would require understanding whether we're dealing with set operations or vector operations and applying the correct algebraic rules.