Property of Complements

For sample space $S$
For $A$ and $A^{c}$ we have $A \cap A^{c} = \emptyset$
But $A \cup A^{c} = S$
$P (A \cup A^{c}) = P (S)$
$1 = 1$
As because of the probability axioms, we have that the probability of the sample space is $1$ .
We can also use the additive property.
- $P (A) + P (A^{c}) - P (A \cap A^{c}) = 1$