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| x 1 y +z y 1 z+x z 1 x+y|

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a

1+x+y+z

b

x +y +z

c

0

d

1

answer is C.

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Detailed Solution

| x 1 y +z y 1 z+x z 1 x+y| C1→C1+C2+C3 1+x+y+z1y+z1+x+y+z1z+x1+x+y+z1x+y=(1+x+y+z)|11y+z11z+x11x+y|=0

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| x 1 y +z y 1 z+x z 1 x+y|