Implication and Iff
The Symbols are and
Implication says "if ... then"
If both a and b are odd numbers then (a+b) is even
can be written as:
both a and b are odd numbers (a+b) is even
The reason it points to the right is that it might not be true the other way
Just because (a+b) is even does not mean that a and b are odd (they may both be even)
Iff says "if and only if"
It is an implication that goes both ways.
x + y = 3 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 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.