Answer the True or False Questions Based on Algebra

True or False

  1. True or false. A set is any collection of objects.
  2. True or false. A proper subset of a set is itself a subset of the set, but not vice versa.
  3. True or false. The empty set is a subset of every set.
  4. True or false. If A ∪ B = ∅ , then A =  ∅ and B =  ∅ .
  5. True or false. If A ∩ B =  ∅ , then A =  ∅ or B =  ∅ or bothA and B are empty sets.
  6. True or false. (A ∪ Ac)c =  ∅ .
  7. True or false. [A ∩ (B ∪ C)]c= (A ∩ B)c   (A  ∩ C)c
  8. True or false. n(A) + n(B) = n(A  ∪ B) +n(A  ∩ B)
  9. True or false. If A ∈ B, then n(B) =n(A) + n(Ac ∩ B).
  10. True or false. The number of permutations of n distinct objects taken all together is n!
  11. True or false. P(nr) = rC(nr).

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