Checking my Boolean expression simplification

[Fatima Hasan]

Homework Statement

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Homework Equations

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The Attempt at a Solution

Could someone check my answer please ?

 

[verty]

I get the same answer:

$F = x + \lnot x(\lnot xw + x\lnot w)$
$= x + \lnot x\lnot xw + \lnot xx\lnot w$
$= x + \lnot xw$
$= x + w$