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solve the Boolean function

hi, i was trying to solve the boolean fuction and i do not know if i did it right. can someone please take a look at it and give me your comments?

F=xy'z + x'y'z + xyz
=xy'z + xyz + x'y'z //rearrange
=xz(y'+y)+x'y'z
=xz + x'y'z
=xz(1+y) + x'y'z
=xz+xyz+x'y'z
=xy+z(xy+x'y')
=xz+z
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