Question

Let A, B, C be any three non-empty sets. If A $\cup$ B = A $\cup$ C, then which one of the following is definitely true?

• A. B = C
• B. $B\subseteq C$
• C. $C\subseteq B$
• D. none of these

Answer 1

Answer: (D)

This can be understood by giving one example.
Let Let A = {1, 2, 3}, B = {1, 3, 4, 5} and C = {2, 4, 5}.
$A\cup B$ = {1, 2, 3, 4, 5} and $A\cup C$ = {1, 2, 3, 4, 5}
but $B\ne C$
B is not a subset of C and C is not a subset of B