"This is cheese, and this is a sandwich with cheese."
Translation:Це сир, а це бутерброд з сиром.
І connects sentences or words. А connects only sentences.
І connects sentences that are "alike", А connects sentences that that are "opposite" or not alike
The meaning of а is kind of between "and" and "but" in English. Very often you can translate а as either "but" or "and".
It's all about the agreement between the subjects, verbs and objects of the two sentences you want to connect:
Ти любиш макарони, і ти любиш/ненавидиш рис (the subject is the same, so nothing else matters) (ненавидиш = hate)
Ти любиш макарони, і вона любить макарони (both love; both love pasta)
Ти любиш макарони, а вона ненавидить макарони (both are about pasta, but the action is different)
Ти любиш макарони, а вона любить рис (the action is the same, but the object is different)
Ти любиш макарони, а вона ненавидить рис (everything is different)