# Questions tagged [question-verification]

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### Let $X$ be a set with $n$ elements. Prove that $\sum_{Y, Z \subseteq X}|Y \cap Z|=n \cdot 4^{n-1}$

Let $X$ be a set with $n$ elements. Prove that $$\sum_{Y, Z \subseteq X}|Y \cap Z|=n \cdot 4^{n-1}$$ The sum is over all possible pairs $(Y, Z)$ of subsets of $X$. I do not need a solution, but ...
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### "General" vs "Galois" Triple Plane

Suggested solution from comments: The curves $R$ and $R_0$ in the definition of "general" triple planes are usually assumed to be different. I am currently working in the following setting: ...
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### Are these test paper questions as unclear and ambiguous as I think they are?

The Local Education Authority here in Wales are running a free voluntary course online for maths dunces like me to help us to help our 7-14 year olds with maths. There's a free optional paper leading ...
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### What does c mean in the following question on cardinality?

I found a question in Modern Real Analysis by William P. Ziemer. The question can be found in Section 2.1 Question 1. It goes: Use the fact that $\mathbb N =$ {$n: n = 2k$ for some $k \in \mathbb N$} ...
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### If $2\cos\alpha_1=a+ \frac1a$ ,$2\cos\alpha_2 =b+ \frac1 b$ , etc... then show that $abc +\frac{ 1}{ abc} + ... = 2 \cos(\alpha_1 + \alpha_2 + ...)$
If $2\cos\alpha_1=a+\frac1a$,$2\cos\alpha_2 =b+\frac1b$, etc... then show that $abc +\frac{1}{abc} + ... = 2 \cos(\alpha_1 + \alpha_2 + ...)$ I don't get how to solve this problem. I tried the ...