Is this proof incomplete? Can it be worded better?
Let A and B be disjoint sets. Prove that A = (A ∪ B) - B
First, we show that A ⊆ (A ∪ B) − B. Let x ∈ A. Since A ∩ B = ∅, it follows that x / ∈ B.
Therefore, x ∈ A ∪ B and x / ∈ B; so x ∈ (A ∪ B) − B. Thus A ⊆ (A ∪ B) − B.
Next, we show that (A ∪ B) − B ⊆ A. Let x ∈ (A ∪ B) − B. Then x ∈ A ∪ B and x / ∈ B. From this, it
follows that x ∈ A. Hence (A ∪ B) − B ⊆ A.
I feel as if I'm missing some simple intermediary steps. My audience for this proof has pretty basic understanding of proofs
proof-verification
asked Nov 19 '18 at 4:31
T. Joe
62
add a comment |
Let A and B be disjoint sets. Prove that A = (A ∪ B) - B
First, we show that A ⊆ (A ∪ B) − B. Let x ∈ A. Since A ∩ B = ∅, it follows that x / ∈ B.
Therefore, x ∈ A ∪ B and x / ∈ B; so x ∈ (A ∪ B) − B. Thus A ⊆ (A ∪ B) − B.
Next, we show that (A ∪ B) − B ⊆ A. Let x ∈ (A ∪ B) − B. Then x ∈ A ∪ B and x / ∈ B. From this, it
follows that x ∈ A. Hence (A ∪ B) − B ⊆ A.
I feel as if I'm missing some simple intermediary steps. My audience for this proof has pretty basic understanding of proofs
proof-verification
asked Nov 19 '18 at 4:31
T. Joe
62
add a comment |
Let A and B be disjoint sets. Prove that A = (A ∪ B) - B
First, we show that A ⊆ (A ∪ B) − B. Let x ∈ A. Since A ∩ B = ∅, it follows that x / ∈ B.
Therefore, x ∈ A ∪ B and x / ∈ B; so x ∈ (A ∪ B) − B. Thus A ⊆ (A ∪ B) − B.
Next, we show that (A ∪ B) − B ⊆ A. Let x ∈ (A ∪ B) − B. Then x ∈ A ∪ B and x / ∈ B. From this, it
follows that x ∈ A. Hence (A ∪ B) − B ⊆ A.
I feel as if I'm missing some simple intermediary steps. My audience for this proof has pretty basic understanding of proofs
proof-verification
asked Nov 19 '18 at 4:31
T. Joe
62
Let A and B be disjoint sets. Prove that A = (A ∪ B) - B
First, we show that A ⊆ (A ∪ B) − B. Let x ∈ A. Since A ∩ B = ∅, it follows that x / ∈ B.
Therefore, x ∈ A ∪ B and x / ∈ B; so x ∈ (A ∪ B) − B. Thus A ⊆ (A ∪ B) − B.
Next, we show that (A ∪ B) − B ⊆ A. Let x ∈ (A ∪ B) − B. Then x ∈ A ∪ B and x / ∈ B. From this, it
follows that x ∈ A. Hence (A ∪ B) − B ⊆ A.
I feel as if I'm missing some simple intermediary steps. My audience for this proof has pretty basic understanding of proofs
proof-verification
proof-verification
asked Nov 19 '18 at 4:31
T. Joe
62
asked Nov 19 '18 at 4:31
T. Joe
62
asked Nov 19 '18 at 4:31
T. Joe
62
asked Nov 19 '18 at 4:31
T. Joe
62
asked Nov 19 '18 at 4:31
T. Joe
62
62
add a comment |
add a comment |
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