# Union of events?

## Homework Statement

Definition:

A union of events A,B,C, . . . is an event consisting of all the outcomes in all
these events. It occurs if any of A,B,C, . . . occurs, and therefore, corresponds
to the word “or”: A or B or C or ... (Figure 2.1a).

## The Attempt at a Solution

I'm confused at "It occurs if any of A,B,C, . . . occurs"

If the union of events A,B,C... is an event consisting of all outcomes in all of these events, then doesn't that imply that A and B and C and ... have to occur, not A or B or C or ..?

I understand that this is their definition and they can define it anyway they want to, but it seems off for me.

One way I can possibly rationalize this is: say x is an outcome of a union b. and x is an outcome of a but not b. Since x is an outcome of a union b, if x has occured, the event a union b has occured. But also the event A has occured

am I on the right track?

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StoneTemplePython
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I'm confused at "It occurs if any of A,B,C, . . . occurs"

If the union of events A,B,C... is an event consisting of all outcomes in all of these events, then doesn't that imply that A and B and C and ... have to occur, not A or B or C or ..?...
am I on the right track?
No. You are thinking of the intersection operation (which, roughly, is products for sets). The Union operation in some sense is the addition operation for sets.

To understand the definition: draw a 3 circle venn diagram (kind of like the olympics rings) and shade in the first circle blue, second red, third gold. Any and all shaded area is the union of the points in those circles. The intersection is only the very dark color that is that mixture called "blue-red-gold".

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

Definition:

A union of events A,B,C, . . . is an event consisting of all the outcomes in all
these events. It occurs if any of A,B,C, . . . occurs, and therefore, corresponds
to the word “or”: A or B or C or ... (Figure 2.1a).

## The Attempt at a Solution

I'm confused at "It occurs if any of A,B,C, . . . occurs"

If the union of events A,B,C... is an event consisting of all outcomes in all of these events, then doesn't that imply that A and B and C and ... have to occur, not A or B or C or ..?

I understand that this is their definition and they can define it anyway they want to, but it seems off for me.

One way I can possibly rationalize this is: say x is an outcome of a union b. and x is an outcome of a but not b. Since x is an outcome of a union b, if x has occured, the event a union b has occured. But also the event A has occured

am I on the right track?
If A = {all the male students in a class} and B = {all the female students in a class} then A∪B = {all the students in the class}. Very likely there is no student in the class that is in both sets A and B.

FactChecker
Gold Member
You clearly understand what they are trying to say about the definition. That mathematics definition of "union" is universally accepted. You should accept that for the sake of communication of mathematics rather than worrying about other possible interpritations of the English language. Accept it and move on. Save the English discussion for another day.

If A = {all the male students in a class} and B = {all the female students in a class} then A∪B = {all the students in the class}. Very likely there is no student in the class that is in both sets A and B.
Nice! this was the kind of reply I was looking for. And if we have an occurrence of the event {all the male students in a class} then we also have an occurrence of {all the male students in a class} ∪ {all the female students in the class} am i right?

You clearly understand what they are trying to say about the definition. That mathematics definition of "union" is universally accepted. You should accept that for the sake of communication of mathematics rather than worrying about other possible interpritations of the English language. Accept it and move on. Save the English discussion for another day.
Hmm I guess you're right. I waste too much time on insignificant things like this >.>

Mark44
Mentor
Here's an example that might help clarify what is meant by "an event." Consider a six-sided die, with sides identified by one to six spots (or "pips"). There are six possible events: 1 is rolled, 2 is rolled, ..., 6 is rolled.
We could divide these six events into two sets, with E = {an even number is rolled}, and O = {an odd number is rolled}. Each of these sets contains three events. The universal set here is U = E ∪ O, which consists of all six events. Sets E and O are disjoint, meaning that when you roll a die, it can't come up with a number that is both odd and even. Symbolically, that is E ∩ O = ∅, the empty set.

The sets list the different possible events -- they don't say anything about whether the events have occurred or not. .