• Support PF! Buy your school textbooks, materials and every day products Here!

Union of events?

  • Thread starter r0bHadz
  • Start date
  • #1
194
17

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).

Homework Equations




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?
 

Answers and Replies

  • #2
StoneTemplePython
Science Advisor
Gold Member
2019 Award
1,142
542
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".
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

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).

Homework Equations




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.
 
  • #4
FactChecker
Science Advisor
Gold Member
5,315
1,904
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.
 
  • #5
194
17
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?
 
  • #6
194
17
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 >.>
 
  • #7
33,174
4,858
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. .
 

Related Threads for: Union of events?

Replies
4
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
1K
Replies
3
Views
920
Replies
8
Views
2K
Top