1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A, B, C be any three non-empty sets. If A ∪ B = A ∪ C, then which one of the following is definitely true?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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?

Sets

Solution:

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 $B \neq C$
B is not a subset of C and C is not a subset of B