Prove or disprove the following statements:

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a) Every odd number greater than 3 can be written as the sum of two prime numbers.
b) If n is not a multiple of 3, then n² + 2 is a multiple of 3.
c) If n is an odd number, then n² + 4 is prime.
d) If X ⊆ A and Y ⊆ B , then X ∪ Y ⊆ A ∩ B.
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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