AND gate ("ON" and "OFF" are the target values):

                 | \
                 |  \
           OFF   on  \ON
                 |    \
                 |     \
                 |      \
       ----off--------on-\---
                 |        \
                 |         \
                 |          \
           OFF  off  OFF     \
                 |

OR gate ("ON" and "OFF" are the target values):

                 |
      \    ON    on    ON
       \         |
        \        |
         \       |
       ---\off---------on-----
           \     |
            \    |
             \   |
           OFF\ off    ON
               \ |
                \|

XOR gate ("ON" and "OFF" are the target values):

                 |
                 |
           ON    on  OFF
                 |
                 |
       ----off--------on-----
                 |
                 |
           OFF  off   ON
                 |
                 |

We can't find a line to separate the "on" and "off" values in the XOR function.  It haas to be a curve instead.

XOR gate ("ON" and "OFF" are the target values):

                 |
         +----+  |
         | ON |  on  OFF
         |    |  |        
         |    +----------+
       --|-off--------on-|---
         +----------+    |
                 |  |    |
           OFF  off | ON |
                 |  +--- +
                 |