(adsbygoogle = window.adsbygoogle || []).push({}); Proof involving sets. NEED HELP!!!

1. The problem statement, all variables and given/known data

Prove directly "If A U B = A, then B is a subset of A." and also provide a proof by contrapositive of its converse.

2. The attempt at a solution

Here is what i did, but I don't know if it is right or not,

Direct Proof: Assume A U B = A, then x ∈ (A U B) and x ∈ A. So it follows that B ∈ A = B is a subset of A.

Contrapositive of Converse Proof: Assume that A U B ≠ A, then x ∈ (A U B) and x ∉ A. Then, B ∉ A and so B is not a subset of A.

I don't think this is right. Could someone help me out please??

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# Homework Help: Proof involving sets. NEED HELP

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