Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪ A) and B ⊆ D^c, then
Posted: Mon May 02, 2022 12:23 pm
Prove the following statement using element proof:
1. For any four sets A, B, C, and D, if C ⊆ (D ∪ A) and B ⊆ D^c,
then C ∩ B ⊆ A
2. For any three sets A, B, and C, if A ∩ C ⊆ B, then (A − B) ∩
(C − B) = ∅
3. For any three sets A, B, and C, if A ∪ C ⊆ B, then C × A ⊆ B
× B
1. For any four sets A, B, C, and D, if C ⊆ (D ∪ A) and B ⊆ D^c,
then C ∩ B ⊆ A
2. For any three sets A, B, and C, if A ∩ C ⊆ B, then (A − B) ∩
(C − B) = ∅
3. For any three sets A, B, and C, if A ∪ C ⊆ B, then C × A ⊆ B
× B