帮我解答这个题目 并解除正确的答案 我里面所有的都不知道 请告知用到的所有知识点---Question Stem:
1. 设集合 $A=\{1,2,3\}, B=\{x|y=\frac{1}{\ln(x-1)}+\sqrt{3-x}\}$, 则集合 $A \cap B$ 的元素个数为
Options:
A. 3
B. 2
C. 1
D. 0
Other Relevant Text:
None other than the question number and the content of the sets and options.
Mathematical Formulas/Expressions:
Set A: $A=\{1,2,3\}$
Set B definition: $B=\{x|y=\frac{1}{\ln(x-1)}+\sqrt{3-x}\}$
Function definition within set B: $y=\frac{1}{\ln(x-1)}+\sqrt{3-x}$
Intersection to find: $A \cap B$
Chart/Diagram Description:
None present.