How do I prove/ find counterexamples for the following?
Dom(R∩S)=Dom(R)∩Dom(S)
Rng(R∩S)=Rng(R)∩Rng(S)
Dom(R-S)=Dom(R)-Dom(S)
Rng(R-S)=Rng(R)-Rng(S)
I know how to prove Dom(R∪S)=Dom(R)∪Dom(S)and Dom(R∩S)=Dom(R)∩Dom(S), but am unsure with how to proceed with these. Could someone provide hints/ preliminary steps for each?
I also believe that all are true and can be proven.. is this not the case?