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.