1. The problem statement, all variables and given/known data This excresice is supposed to help you understand the basic operations of sets, later used in probability. I am given the following phrases and have to write them in using mathematics. Given three events A, B and C, which belong to sample space S, calculate the following events: a) Only A happens b) A and B happen, but not C c) At least one of the events happen d) At least two of the events happen e) All the events happen f) None of the events happen g) One of the events happen at most h) Two of the events happen at most i) Exactly two of the events happen j) Three of the events happen at most 2. Relevant equations No needed. 3. The attempt at a solution Here are my solutions. Of course I want to know if I'm correct or not, but I basically need some help with g, h and k. I can't quite understand these expressions and when I try to turn them into mathematical expressions I end up with nonsense. I also used Venn diagrams to understand each event better. a) A∩B'∩C' b) This translates to "Only A and B happen", so A∩B∩C' c) This translates to "A or B or C or all of them", so A∪B∪C d) "Two or more events happen at the same time", so (A∩B)∪(A∩C)∪(B∩C) e) A∩B∩C f) Meaning "... at the same time", so A'∩B'∩C' or (A∪B∪C)' from De Morgan's Law. g) I can't wrap my head around this one. I'd think it this way: This translates to "Two or more events can't happen at the same time", so I'd go full boolean and think " NOT(A AND B) AND NOT(A AND C) AND NOT(B AND C) AND NOT(A AND B AND C)". Is this correct? Is there any other way to make me understand it? The Venn Diagram helps me get it better, but I could still use some further explaination. h) This one seems easier to understand if I translate it to "Three events can't happen at the same time, so it's simply (A∩B∩C)' or (A'∪B'∪C') from De Morgan's Law. The Venn Diagram of this also makes sense to me. i) This one looks easy using the Boolean logic again. (A AND B AND NOT C) OR (A AND NOT B AND C) OR (NOT A AND B AND C). j) This makes the less sense, since there are three events. I honestly can't think of anything.