Boolean Algebra

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Prove the following Boolean expression using the laws and theorems of Boolean algebra.

`("A" + "B") ("A" + overline"B")` = A

Prove the following Boolean expression using the laws and theorems of Boolean algebra.

`"A" (overline"A" + "B")` = AB

Prove the following Boolean expression using the laws and theorems of Boolean algebra.

(A + B) (A + C) = A + BC

Verify the given Boolean equation A + `overline"A""B"` = A + B using truth table.

Write down the Boolean equation for the output Y of the given circuit and give its truth table.