John and Sophia roll a die and consider the outcome. They denote the set of all possible outcomesΩ={1, 2, 3, 4, 5, 6}.In probability theory, this set of all possible outcomes is called the sample space, but a general collection of outcomes is called an event.John and Sophia are interested in the following events:ABCD===={1, 3, 5}{2, 4, 6}{1}{6}.Tick the most appropriate answer:A⊆CA∪C=BB⊆DA∪D=∅Ω∪A=AA∖C=AC⊆A

Let's go through each of the options:

A⊆C: This means that every element in A is also in C. Looking at the sets, A={1, 3, 5} and C={1}. Not every element in A is in C, so this is false.

A∪C=B: This means that the union of A and C equals B. The union of A and C would be {1, 3, 5}, and B={2, 4, 6}. These are not equal, so this is false.

B⊆D: This means that every element in B is also in D. Looking at the sets, B={2, 4, 6} and D={6}. Not every element in B is in D, so this is false.

A∪D=∅: This means that the union of A and D is the empty set. The union of A and D would be {1, 3, 5, 6}, which is not the empty set, so this is false.

Ω∪A=A: This means that the union of Ω and A equals A. The union of Ω and A would be {1, 2, 3, 4, 5, 6}, which is not equal to A={1, 3, 5}, so this is false.

A∖C=A: This means that the difference of A and C equals A. The difference of A and C would be {3, 5}, which is not equal to A={1, 3, 5}, so this is false.

C⊆A: This means that every element in C is also in A. Looking at the sets, C={1} and A={1, 3, 5}. Every element in C is in A, so this is true.