How can I prove the Boolean algebraic rule $$A+A'B=A+B$$ without using a truth table?
With the truth table, it is easy to see that the two are equal, but how can I prove it using lesser Boolean identities?
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Use the distributivity of $\lor$ (sum) over $\land$ (product), which is unique to Boolean algebra: $$A+A'B=(A+A')(A+B)=A+B$$
Parcly Taxel
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Expand: $(A + A')(A + B) = AA + AB + A'A + A'B = A + AB + A'A + A'B = A(1 + B) +0 + A'B = A + A'B$ – Tom Collinge Nov 07 '16 at 07:38