How to Solve a Boolean Equation with a Bar Above One Variable?

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To solve the Boolean equation AB(A + B̅) = X, apply the distributive property of meet over join. Recognize that meet and join are symmetrical, allowing for variable interchange. Utilize properties of Boolean algebra, such as the meet of a variable with itself and with its negation. The simplification leads to AB(A + B̅) = AB + A(0), resulting in AB. The final expression confirms that X equals AB.
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I was just wondering if anyone could lend me some guidence in the boolean equation AB(A+B)= X when the last "B" in the formula has a bar above it.. thanks
 
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If juxtaposition stands for "meet" and + stands for "join," then you can use the distributivity of meet over join to get an expression without any parentheses. Then use that fact that meet and join are each symmetrical so that you can interchange the variables on either side. Then use what you know about thiings such as the meet of a variable with itself, and the meet of a variable with its negation. I think I know what the answer is, but I'll let you take it from here.
 
AB(A + \overline{B}) = ABA + AB\overline{B} = AB + A(0) = AB
 

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