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# Uniting Theorem #1

This is (for my way of thinking as a physicist) best thought of in terms of logic gates.

 . + = Here we have and as inputs into an AND gate. The output of this is then ORed with . Either input to the OR gate has to high for the output to be high... and as alone being high would have no effect (as it cannot alone control the output of the AND gate), it is only the state of that matters. When is high the output is high, when it is low the output is low - the output follows - therefore only is required. You can do this by using Boolean algebra to simplify the expression: A.B + A = A(B + 1) (B + 1) = 1 (Law of 1s and 0s) = A(1) = A (Identities) ( + ). = Here we have and as inputs into an OR gate. The output of that is then one of the inputs into an AND gate. alone being high would have no effect (as it cannot alone control the output of the AND gate), it is only the state of that matters. When is high the output is high, when it is low the output is low - the output follows - therefore only is required. You can do this by using Boolean algebra to simplify the expression: (A + B).A = AA + BA AA = A (Indempotence) = A + BA = A(1 + B) (1 + B) = 1 (Laws of 1s and 0s) So, (A + B).A = A