# How many points are there in the following set? [closed]

Let us consider the following set:

$$A=\{(x, y, z) \in \Bbb{R}\times\Bbb{R}\times\Bbb{R} : ax+by+c=0,z=0 \},c\neq 0$$ and $$B=\{(x, y, z) \in \Bbb{R}\times\Bbb{R} \times\Bbb{R} : ax+by=0,z=0\}$$. Then $$A, B$$ are two infinite sets. How to determine the cardinality of the set $$A-B$$?

## closed as off-topic by Saad, spaceisdarkgreen, Brahadeesh, I am Back, DidDec 1 '18 at 17:10

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Saad, spaceisdarkgreen, Brahadeesh, I am Back, Did
If this question can be reworded to fit the rules in the help center, please edit the question.

I am assuming $$a$$, $$b$$, and $$c$$ are fixed real numbers.
If $$(x,y,z)\in B$$, then $$z=0$$ and $$ax+by=0$$. But then $$ax+by\neq -c$$, since $$c\neq 0$$, so $$(x,y,z)\not\in A$$. Therefore, $$A-B=A$$.