Perceptron Primitive Boolean Functions
I interpret it as the input takes binary value $0$ (false) and $1$ (true) while the output take $-1$ (false) and $1$ (true).

The map is $$sign\left(\sum_{i=1}^nw_ix_i+w_0\right).$$

If we let $w_i=0.5, i \ge 1$, then we have the mapping rule to be 

$$sign\left(\frac12\sum_{i=1}^nx_i+w_0\right).$$

For the AND operator, if we set $w_0=-0.8$, for it to take positive value both $x_i$ has to be $1$.

For the OR operator, if we set $w_0=-0.3$, we just need one of them to take positive value for it to be true.