Prove that union of two ideals is an ideal if one of the ideals is contained within the other

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Prove that union of two ideals is an ideal if one of the ideals is contained within the other

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  1. Prachi Mishra
  2. Union of ideal may not be an ideal
  3. Prove that union of two ideals is an ideal if one of the ideals is contained within the other
  4. Let A and B are two ideal then A Union B is also an ideal
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Conversely:
Given: AUB is an ideal and either A is contained in B or B is contained in A
To prove: A and B are ideal
AUB is ideal (given)
And A is contained in B (given)
So, AUB = B
B is an ideal since AUB is ideal
Similarly,
AUB is ideal (given)
And B is contained in A (given)
So, AUB = A
A is an ideal since AUB is ideal

prachi_
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👍, nice, ...prr Converse me ye kaise show karenge ki A is contained in B and vice versa, bta dijiye please,

monikachauhan