Final answer:
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.