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### Chocolate or Vanilla Ice Cream

```Date: 10/22/2002 at 09:25:29
From: Sue Smouse
Subject: "either/or" type of 4th grade word problem

I have looked for a rule to follow to help explain this to myself,
but I give up. I believe it should be pure addition and the sum of the
two numbers would be the answer.

In a recent survey, 1550 people said they liked only chocolate ice
cream and 2550 said they liked only vanilla. How many people liked
either chocolate or vanilla ice cream?

Is the answer 4100?  Is there a formula/rule you follow to figure it
out? Thank you!
```

```
Date: 10/22/2002 at 11:31:08
From: Doctor Ian
Subject: Re: "either/or" type of 4th grade word problem

Hi Sue,

The rule is that you take the union of the two sets, which contains
all the elements in both sets.

Normally, you have to take into account elements that might be in both
sets. For example, suppose we divide some people into males and
females:

males   = {Bob, Ted}
females = {Carol, Alice}

The union of the two sets is

males U females = {Bob, Carol, Ted, Alice}

and the size of the union is just the sum of the sizes of the sets.
But this is ONLY true because the sets have no elements in common.
Suppose we divide the same people up according to foods that they
like:

likes_pizza  = {Bob, Carol, Ted}
likes_quiche = {Carol, Ted, Alice}

The union is

likes_pizza U likes_quiche = {Bob, Carol, Ted, Alice}

but note that it's SMALLER than the sum of the sizes of the input
sets, because Carol and Ted are members of both sets. The general
rule is

size (this U that) =   (number elements in this)
+ (number of elements in that)
- (number of elements in both this and that)

In your example, there seems to be no one who likes both flavors, so
there's nothing to subtract.

Does this make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 10/23/2002 at 21:03:10
From: Sue Smouse
Subject: Thank you ("either/or" type of 4th grade word problem)

Dear Dr. Ian,

Thank you so very much for your super response to my question!  It was
the exact explanation I was searching for.
```
Associated Topics:
Elementary Word Problems

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