# MandysNotes

Tuesday, 18 March 2014 00:00

## Implication

By  Gideon
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Suppose we are looking for an animal, but all we know about it is that it either does not have a duck bill, or it is a mammal.

We write this as

"(not A) or B"

$= \left( \lnot A \right) \cup B$

$= A \rightarrow B.$

Now suppose that the animal turns out to have a duck bill: then it must be a mammal (in this case a platypus).

On the other hand, if it is not a mammal, then it cannot have a duck bill.

Now consider the set of animals that either are not mammals, or have duck bills.

This is the set "(not B) or A"

$= \left( \lnot B \right) \cup A$

$= B \rightarrow A.$

Now suppose that the animal is indeed a mammal: then it must have a duck bill.

On the other hand, suppose the animal does not have a duck bill: then it cannot be a mammal.