Logic

Truth Tables

~ not (negative)

A and Both (conjunction

V or please note that an or is really an OR and an AND

→ If then (conditional)

↔ If and only if (biconditional)

Here is an example that you need a VENN Diagram to help you solve. It is a bit involved - so be patient.

A local television station sent out questionnaires to determine if viewers would rather see a documentary,

an interview show, or reruns of a game show. There were 850 responses with the following results:

How many are interested in exactly one kind of show? ANSWER: 408

How did we get this answer? I created a Venn Diagram for each of the bullet points above

Then I numbered each of the area's so I could see where we had just one area - and then do the math to see if I could solve for the other areas

Then I combined the info from both of these diagrams and put it into a spreadsheet (I like using spreadsheets because it is very visual)

Calculators are not as visual to me. You can't see the whole picture.

Each area in the Zenn Diagram got a number - as I figured out the single areas:

Area 2 was 255 (255 were interested in an interview show AND documentary, but not reruns)

Area 3 was 34 ( 34 were interested in an interview show and reruns but not a documentary)

Then you could start to fill in the other areas

Area 4 is part of (51 were interested in an interview show AND reruns = Part 3 + Part 4) 51-34 = 17

which helped me find Area 6

You keep going until the grid is filled - see image below:

Now that you have all the numbers to fill your Zenn Diagram

you can answer the question:

How many are interested in exactly one kind of show?

On the Venn Diagram - the areas that are ONE KIND are Area-1, Area-5 and Area-7

170 + 187 + 51 = 408 the correct ANSWER: 408

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