For any two sets A and B prove that... B is a subset of A union B. and A union B is a subset of A.
Answers & Comments
AshishRana
Hey there!! the solution to your question is as follows:
Consider two sets namely 'A' and 'B'. Let A contain some elements such that A = {1,2,3,4,5,6,7,8} Similarly, let B contain some elements such that B = { 5,6,7,8}
then A U B ( A union B) = {1,2,3,4,5,6,7,8} ( In a union of two sets, we take all the distinct elements of two sets and form a new set that has the elements of both sets.
Now comparing set B with (A U B ), we find that all the elements of set B {5,6,7,8} are present in set (A U B).
This makes set 'B' a subset of (A U B) (When all the elements of a set are present in another set, then this set is called a subset of the other set.)
Now coming to the other part of the question. As we saw that Set 'A' in itself includes all the elements of (A U B) i.e {1,2,3,4,5,6,7,8} even before taking the union of set 'A' and set 'B'.
This means that all the elements of (A U B) are included in the set A. This makes (A U B), a subset of set A.
Hope it helps. :)
57 votes Thanks 39
AshishRana
thanks for marking it the brainliest. :)
Answers & Comments
Consider two sets namely 'A' and 'B'.
Let A contain some elements such that A = {1,2,3,4,5,6,7,8}
Similarly, let B contain some elements such that B = { 5,6,7,8}
then A U B ( A union B) = {1,2,3,4,5,6,7,8}
( In a union of two sets, we take all the distinct elements of two sets and form a new set that has the elements of both sets.
Now comparing set B with (A U B ), we find that all the elements of set B {5,6,7,8} are present in set (A U B).
This makes set 'B' a subset of (A U B)
(When all the elements of a set are present in another set, then this set is called a subset of the other set.)
Now coming to the other part of the question. As we saw that Set 'A' in itself includes all the elements of (A U B) i.e {1,2,3,4,5,6,7,8} even before taking the union of set 'A' and set 'B'.
This means that all the elements of (A U B) are included in the set A. This makes (A U B), a subset of set A.
Hope it helps. :)
Step-by-step explanation:
hope this will help you a lot . thanks