Implication and Iff

The Symbols are implies symbol and iff symbol

Implication: implies symbol

Implication says "if ... then"

Example:

If both a and b are odd numbers then (a+b) is even

can be written as:

both a and b are odd numbers implies symbol (a+b) is even


The reason it points to the right is that it might not be true the other way

Example:

Just because (a+b) is even does not mean that a and b are odd (they may both be even)

 

Iff: iff symbol

Iff says "if and only if"

It is an implication that goes both ways.

Example:

x + y = 3 iff symbol x = 3 − y

That one is true both ways!

Example: for a and b both integers

If one of a and b is odd and the other is even, then a+b is odd

Can also be written:

One of a and b is odd and the other is even iff symbol a+b is odd

In this case it goes both ways, because if a+b is odd then one of a or b must be odd and the other even.

 

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Algebra Index