Can anyone please give me an idea to disprove the following with a counterexample:
$A , B , C$ are sets. If $A \times C = B \times C$ , then $A = B$. (Here $\times$ is a Cartesian product.)
I tried giving random numbers in Venn diagram, but that didn't work. And, using subset way to prove equal, I still couldn't solve it.
In cases like this, you need to look at the extreme ends. Here's a hint: Pretend like it was multiplication. Find numbers to disprove if $a\cdot c=b\cdot c$ then a=b. What would make that equation fail? Put that into set theory.