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arpitm08
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Proof involving sets. NEED HELP!
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??
Homework Statement
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??