Sets and subsets

  1. Prove that for any set TeX Embedding failed!, TeX Embedding failed!
  2. Prove that TeX Embedding failed!
  3. Prove that for any set TeX Embedding failed!, TeX Embedding failed!.
  4. Determine whether each of the following statements is true or false:
    1. For each set TeX Embedding failed!, TeX Embedding failed!.
    2. For each set non-empty set TeX Embedding failed!, TeX Embedding failed!.
    3. For each set TeX Embedding failed!, TeX Embedding failed!.
    4. For each set TeX Embedding failed!, TeX Embedding failed!.
    5. For each set TeX Embedding failed!, TeX Embedding failed!.
    6. There are no members of the set TeX Embedding failed!.
    7. Let TeX Embedding failed! and TeX Embedding failed! be sets. If TeX Embedding failed!, then TeX Embedding failed!.
    8. There are two distinct objects that belong to the set TeX Embedding failed!
  5. Let TeX Embedding failed!,TeX Embedding failed!,TeX Embedding failed! be sets. Prove that if TeX Embedding failed! and TeX Embedding failed! then TeX Embedding failed!.
  6. Let TeX Embedding failed! be sets. Prove that if TeX Embedding failed! and TeX Embedding failed!, then TeX Embedding failed!.