Question

for any two sets A and B , A union B =A ,if
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Answer 1

Answer:

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Step-by-step explanation:

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.