Question 156
Let $X$ be a set with $n$ elements and let $A_{1}, A_{2}, \ldots, A_{n}$ be different subsets of $X$. Show: There is a $x \in X$ such that the sets
$$
A_{1} \backslash\{x\}, A_{2} \backslash\{x\}, \ldots, A_{n} \backslash\{x\}
$$
all are different.
$$
A_{1} \backslash\{x\}, A_{2} \backslash\{x\}, \ldots, A_{n} \backslash\{x\}
$$
all are different.