A possible way:
If , suppose (without loss of generality) that
analyzing the cases
Please forgive me in advance if this post is not in the correct section!! Anyways, one of my homework problems is to show that the symmetric difference Δ satisfies the cancellation law, namely, if AΔB=AΔC then B=C. It seems like this is fairly simple however I just can't seem to figure out what to do with this. Thank you for your help!