About set identities

Question

Does associative properties follows only when all the operators in the given expression same (union or intersection) or it do follows when there are different symbols present in the given expression.

E.g.

a U (b U c) U d  =  a U b U (c U d) ;

(a U b) /\ c U d  =  a U (b /\ c) U d.

Answer 1

Associative properties follows only when symbols are same

You can take this example

A ={1,2,3}

B= {3,4,5}

C={1,3}

(AUB)∩C = {1,3}

AU(B∩C) = {1,2,3}

so we can see that both are not equal.

(AUB)∩C ≠ AU(B∩C)