Question

topic is OPERATIONS ON SETS
Question is Verify
(a) X U ( Y U Z ) = (X U Y) U Z
(b) X intersection (Y intersection Z)=(X intersection Y) intersection Z ,
when
X= {-1,0,2,4,5},
Y={1,2,3,4,7}
Z={4,6,8,10}
answer in detail please ​

Answer 1

Step-by-step explanation:

A:

XU(YUZ)=(XUY)UZ

LEFT HAND SIDE:

(YUZ)={1,2,3,4,7}u{4,6,8,10}

={1,2,3,4,6,7,8,10}

XU(YUZ)={-1,0,2,4,7}U{1,2,3,4,6,7,8,10}

={-1,0,1,2,3,4,6,7,8,10}

RIGHT HAND SIDE:

(XUY)={-1,0,2,4,5}u{1,2,3,4,7}

={-1,0,1,2,3,4,5,7}

(XUY)UZ={-1,0,1,2,3,4,5,7}U{4,6,8,10}

={-1,0,1,2,3,4,5,6,7,8,10}

LEFT HAND SIDE=RIGHT HAND SIDE

HENCE PROVED!