Truth Table for Implication

I was surprised the binary implication operator (→), also called the conditional, has a truth table, just as the AND and OR logical operators do. It is as follows:

A B (A→B)
0 0  1
0 1  1
1 0  0
1 1  1

That is, we can only say something about B if A is true. There is a similar table for the binary biconditional operator (↔):

A B (A↔B)
0 0  1
0 1  0
1 0  0
1 1  1

This means we can determine truth tables for compound statements such as A→(B→C).