Let A, B, and C be sets in a universal set U. We are given n(U) =100, n(A) =28, n(B) =25, n(C) =25, n(A ∩ B) =13, n(A ∩ C) =14, n(B ∩ C) =11, n(A ∩ B ∩ C) =6. What is n(Ac ∩ B ∩ Cc)?  (Enter answer as a whole number)

Q: . If A and B are sets in a universal set U, then AUB=AnB.

A: We proved this by wave diagram

Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: Let A and B be sets. 1) If |A| = 30, |B| = 17, and |A n B| = 2, then |A U B| = 45 2) If |A U B| =…

A:

Q: For any sets A and B , (ANB) = %3D O a. ANB O b. ANB Oc. B-A С. В- А O d. U-B

A: By using identities of set theory :

Q: (d) An (BNC) = (Ar (e) If A C B, then (AUC) C (BUC) (f) ACB if and only if (AUB) = B

A:

Q: 5) Find the union of four sets AUBUCUD, given A= {-3, -2, -1, 0}, B= {-2, -1, 0, 1}, C= {2, 3, 4)…

A: To find union of given four sets.

Q: 6. Let A, B, and C be sets. Verify the following (you can use a membership table) a) An (BUC) =…

A: ∩ : and  ∪ : or  We have to prove :

Q: 7. (12 points) Use a proof by contradiction to prove: For all sets A, B, and C (A\C)n(B\C)n(A\B) = 0

A: Step 1: proof  let (A/C)∩(B/C)∩(A/B)=Φ this means ∃x∈(A/C)∩(B/C)∩(A/B) Step 2:⇒x∈A/C,x∈B/C,x∈A/B…

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: Let the Universal Set, S, have 113 elements. A and B are subsets of S. Set A contains 77 elements…

A: From the provided information, n(U) = 113, n(A) = 77, n(B) = 17 And n (A Ո B) = 13

Q: What can you say about the sets A and B if AB=A?

A: Consider two sets A  and B. Then the symmetric difference between these two sets is denoted by A⊕B.…

Q: A and B be two sets, and A - B = . a) What can you say about sets A and B? b) Draw a Venn diagram.

A:

Q: Consider the following statement: 3x, y, x+y= y. From the options provided below, which universal…

A: Given statement  , x+y = y  So it means there exist x such that for all y x + y = y x = 0

Q: Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B…

A: Consider the given sets:

Q: Describe the following sets in words and/or pictures: 1. {(x,y,z): y = x2 } 2. {(x,y,z): y > z }…

A: Here, to describe the given sets in words and/or picture.

Q: If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :(i) A = {a, b, c} (ii)…

A: Given:

Q: use a Venn diagram to determine which relationship, C, =, or 2, is true for the pair of sets. AUB,…

A:

Q: 2.) Suppose A is a set with 4 elements and B is a set with 3 elements. How many relations are there…

A:

Q: In this problem, you will get some practice with the logic of sets, i.e., ways of putting sets…

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Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 32, n(B) = 33, n(C) =…

A:

Q: 4. Find all subsets of S = {0, 1, {0,1}} which are not also elements of S. (Another way of writing…

A: 4. Given set is S=∅, 1, ∅, 1.   To Find: All subsets of S which are not also elements of S i.e., all…