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Here the presence of a 1 or 0 has no effect. It is the complementary rule to the rule of 1s and 0s where the 1 and 0 has a 'swamping' effect - it totally takes over the output.

This is (for my way of thinking as a physicist) best thought of in terms of logic gates. Linking the 1 or 0 to the signal has no effect - so you may as well remove the logic gate.

. =

Here we have and as inputs into an AND gate. Both inputs have to high for the output to be high... and as one of them IS high the output will depend on the state of alone.

1
Output
0
1
0
1
1
1

 

+ =

Here we have and as inputs into an OR gate. If either input is high the gate output will be high... and as one of them is always low the output will depend on the state of alone.

0
Output
0
0
0
1
0
1