let E,F and G be three events. state expressions fo rthe events.

a. only F occurs
b. exactly two of the events occur.
c. at leasat one of the events occur.
d. E and G occur but F does not.

how do I go about writing these. do I use like union and intersection?

Yes, you can use concepts of set operations such as union (∪), intersection (∩), and complement (') to write expressions for the given events. Here's how you can approach each event:

a. Only F occurs: This means that F occurs, but neither E nor G occurs. The expression for this event can be written as: F ∩ E' ∩ G'

b. Exactly two of the events occur: This means that only two events occur, and not the third. You can express this event as the union of all possible combinations of two events occurring, while the third event does not occur. The expression for this event can be written as: (E ∩ F' ∩ G') ∪ (E' ∩ F ∩ G') ∪ (E' ∩ F' ∩ G)

c. At least one of the events occur: This means that at least one of the events E, F, or G occurs. The expression for this event can be written as the union of all three events. The expression for this event can be written as: E ∪ F ∪ G

d. E and G occur but F does not: This means that both E and G occur, but F does not occur. The expression for this event can be written as: E ∩ G ∩ F'

By using set operations, you can combine events, exclude events, or find the intersection of events to express various conditions.