SOLUTION: By consructing an example of your own verify the fact that for 3 events in the same sample space S. Prove AUB=AUC need not imply that B=C

Algebra ->  sets and operations -> SOLUTION: By consructing an example of your own verify the fact that for 3 events in the same sample space S. Prove AUB=AUC need not imply that B=C      Log On


   

Question 1059557: By consructing an example of your own verify the fact that for 3 events in the same sample space S. Prove AUB=AUC need not imply that B=C
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let A = {1,2}
let B = {2,3}
let C = {1,3}

it's clear that B is not equal to C because B contains {2,3} and C contains {1,3}.

the element 3 is common, but the elements 1 and 2 are not.

A union B is equal to {1,2,3}

A union C is equal to {1,2,3}

the unions are equal, but the individual sets of B and C are not.

i believe that's what you're looking for.