2. For any sets A and B, if A ? B then A ? B. 3. For any sets A and B, A ? B = A if and only if B ? A. 4. For any sets A, B and C, A ? (B ? C) = (A ? B) ? (A ? C). 5. For any sets A and B, ?A ? B? = ?A? ? ?B?. 6. For any set A, A ? A. 7. For any sets A and B, A ? B ? A and A ? B ? B. 8. There exists a set A such that A ? ?A?. 9. For any set A, ? ? A. 10. There exists a set B, such that B ? ?. 11. For any set A, {?} ? A. 12. For any set A, A ? ?A? = U.
Added by Adri-N P.
Close
Step 1
I will address each statement one by one, explaining whether it is true or false and why. ** Show more…
Show all steps
Your feedback will help us improve your experience
William Mead and 97 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
11. Let A and B be subsets of some universal set U. Prove or disprove each of the following: (a) A - (A ∩ B^c) = A ∩ B (b) (A^c ∪ B)^c ∩ A = A - B (c) (A ∪ B) - A = B - A (d) (A ∪ B) - B = A - (A ∩ B) (e) (A ∪ B) - (A ∩ B) = (A - B) ∪ (B - A)
Adi S.
(a) If {1} ∈ P(A), then 1 ∈ A but {1} ∉ A. (b) If A, B and C are sets such that A ⊂ P(B) ⊂ C and |A| = 2, then |C| can be 5 but |C| cannot be 4. (c) If a set B has one more element than a set A, then P(B) has at least two more elements than P(A). (d) If four sets A, BC and D are subsets of {1, 2, 3} such that |A| = |B| = |C| = |D| = 2, then at least two of these sets are equal
Madhur L.
Let the universal set be U = {0,1,2,3,4,5,6,7,8,9}. Create two sets of your choice; call them A and B. Find the following sets. The first set is the complement of the union of sets A and B. The second set is the complement of A intersected with the complement of B. In set notation, this is written: ̅A∧B̅ and Ā ∩ B̄. Repeat part a with two different sets, A and B. Show that the complement of the union of sets A and B is equal to the complement of A intersected with the complement of B for any universal set, U, and any two sets, A and B. In set notation, this is written: ̅A∧B̅ = Ā ∩ B̄ for any universal set, U, and any two sets, A and B.
Brian B.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD