Question

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

Answer 1

See explanation...

Explanation:

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

`(a vv b) vv (not a ^^ not b) = top`

If either of `a` or `b` is true, then `(a vv b)` is true and hence:

`(a vv b) vv (not a ^^ not b) = top`

If neither of `a` or `b` is true, then `(not a ^^ not b)` is true and hence:

`(a vv b) vv (not a ^^ not b) = top`

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