Show That the Boolean Function$F \text { given by } F ( x , y , z ) = x ( z + y z ) + y ( \overline { x z } x ) \text { simplifies to } x z + \bar { x } y \text {, by using }$

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x ( z + y z ) + y \cdot \overline{\overline { x z } \cdot x} = x z + x y z + y ( \overline{\overline { x z }} + \bar { x } ) = x z + x y z + x y z + \bar { x } y = x z + x y z + \bar { x } y = x z + \bar { x } y

Show That the Boolean Function $F \text { given by } F ( x , y , z ) = x ( z + y z ) + y ( \overline { x z } x ) \text { simplifies to } x z + \bar { x } y \text {, by using }$

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