Uniting Theorem #2

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 .

If is high the output is high - if it is low then must be high to get a high output - therefore or must be high.

You can do this by using Boolean algebra to simplify the expression.

. + = ( + ).( + ) - Look at the distribution rule.

Now ( + ) = - Look at the Laws of 1s and 0s

So, . + = .( + ) - Look at the identities we can ditch the '1'

= + - Look at the commutativity rule

(

Here we have and as inputs into an OR gate. The output of that is then one of the inputs into an AND gate.

For the output to be high must be high. But that is not enough, must also be high to get a high output, as when is high the output of the OR gate will depend on the state of - therefore AND must be high.

You can do this by using Boolean algebra to simplify the expression.

( + ). =( .) + (.) - Look at the distribution rule.

( .) = - Look at the Laws of 1s and 0s and we can ditch the '0'

so, ( + ). = . and

( + ). = . - Look at the commutativity rule