163k views
4 votes
Let A,B and C be the sets such that A U B = A U C and A n B = A n C . Show that B=C .

1 Answer

4 votes

Final answer:

To show that B=C, we need to prove that B is a subset of C and C is a subset of B. Starting with B is a subset of C, suppose x is an element of B. This means x is either in A and B or in A and C since A U B = A U C. If x is in A and B, then it is also in A and C because A n B = A n C. Therefore, x is in B and C, which proves that B is a subset of C. Similarly, we can show that C is a subset of B. Therefore, B=C.

Step-by-step explanation:

To show that B=C, we need to prove that B is a subset of C and C is a subset of B. Starting with B is a subset of C, suppose x is an element of B. This means x is either in A and B or in A and C since A U B = A U C. If x is in A and B, then it is also in A and C because A n B = A n C. Therefore, x is in B and C, which proves that B is a subset of C. Similarly, we can show that C is a subset of B. Therefore, B=C.

User Mark Porter
by
8.5k points

No related questions found