Lesson 0110: Proving Equalities

There are many uses for Boolean Algebra. One of them is testing equalities. This is done by taking an equality: and breaking it down into steps.
In this case, that expression is .

Proving equalities involves simplifying the more complicated expression until it is the same as the simpler expression, or until it is completely simplified.
However, like in a proof, reasons have to be given for every step taken when simplifying the more complicated expression.

 AB + AB = 1. The reason for this is that it is "given". AB + (A[not B] + [not A] B) = 2. The reason for this is the rule of [A xor B] AB + A[not B] + [not A] B = 3. The reason for this is the commutative property B(A+[not A]) + A[not B] = 4. The reason for this is the distribuitive property B + A[not B] = 5. The reason for this is the property that states that A + [not A] = 1 A+B= 6. The reason for this is the property that states that B+[not B]A=A+B 7. Therefore AB + AB = A+B

Are the following expressions equal?

1. and

yes
no
2. and

yes
no

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