Question

Given A = (0, 1, 2, 4, 5), B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9} and A $\cup$ (B $\cup$ C) = (A $\cup$ B) $\cup$ C i.e. the union of sets is associative

Type 1 for true and 0 for False

Answer 1

Given, $A=(0,1,2,4,5),B=$ {$0,2,4,6,8$} and $C=$ {$0,3,6,9$}

Union of two sets has all the elements of both the sets

So, $B\cup C=$ { $0,2,3,4,6,8,9$ }
And, $A\cup (B\cup C)=$ { $0,1,2,4,5$ }$\cup$ { $0,2,3,4,6,8,9$ } $=$ { $0,1,2,3,4,5,6,8,9$ } .....(1)
Also, $A\cup B=$ { $0,1,2,4,5,6,8$ }
And, $(A\cup B)\cup C=$ { $0,1,2,4,5,6,8$ }$\cup$ { $0,3,6,9$ } $=$ { $0,1,2,3,4,5,6,8,9$ } .....(2)
From (1) and (2), we know that
$A\cup (B\cup C)=(A\cup B)\cup C$