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De Morgan's Law

Given A = 0, ...

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

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Solution

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
$A \cup (B \cup C) = (A \cup B) \cup C$

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