# How do you prove (a o+ b) o+ (~ a & ~ b) = 1 ?

Mar 8, 2017

See explanation...

#### Explanation:

If I understand your notation correctly, it is what I would express as:

$\left(a \vee b\right) \vee \left(\neg a \wedge \neg b\right) = \top$

If either of $a$ or $b$ is true, then $\left(a \vee b\right)$ is true and hence:

$\left(a \vee b\right) \vee \left(\neg a \wedge \neg b\right) = \top$

If neither of $a$ or $b$ is true, then $\left(\neg a \wedge \neg b\right)$ is true and hence:

$\left(a \vee b\right) \vee \left(\neg a \wedge \neg b\right) = \top$

So under any combination of truth values for $a$ and $b$, the given expression is true.