Math

QuestionSimplify the expression: w=xˉ(x+y)+zˉ+zyw=\bar{x}(x+y)+\bar{z}+z y, where xˉ\bar{x} and zˉ\bar{z} are operations on xx and zz.

Studdy Solution

STEP 1

Assumptions1. The expression to simplify is w=xˉ(x+y)+zˉ+zyw=\bar{x}(x+y)+\bar{z}+z y . The symbols xˉ\bar{x} and zˉ\bar{z} represent some mathematical operation on xx and zz respectively3. The specific operation represented by the bar symbol is not specified and needs to be clarified

STEP 2

In mathematics, the bar symbol over a variable often represents the operation of taking the complex conjugate of a complex number. However, it can also represent other operations such as averaging in statistics or negation in logic. Without specific context, it's impossible to determine the exact operation. For the purpose of this problem, let's assume that the bar symbol represents the negation operation, i.e., xˉ\bar{x} represents "not x" and zˉ\bar{z} represents "not z".

STEP 3

Substitute the assumed operation into the expression.
w=¬x(x+y)+¬z+zyw = \neg x (x+y) + \neg z + z y

STEP 4

Apply the distributive property to the first term to simplify the expression.
w=¬xx+¬xy+¬z+zyw = \neg x \cdot x + \neg x \cdot y + \neg z + z y

STEP 5

In logic, the operation "not x AND x" (represented by ¬xx\neg x \cdot x) is always false. Replace this term with0.
w=0+¬xy+¬z+zyw =0 + \neg x \cdot y + \neg z + z y

STEP 6

implify the expression by removing the0.
w=¬xy+¬z+zyw = \neg x \cdot y + \neg z + z yThis is the simplified expression assuming that the bar symbol represents the negation operation. However, the actual operation could be different depending on the context. Without more information, we cannot further simplify the expression.

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