Let A = {a, b, c},B = {b, c, d},and C = {b, c, e}.(a) Find A ∪ (B ∩ C),(A ∪ B) ∩ C,and (A ∪ B) ∩ (A ∪ C).(Enter your answer in set-roster notation.) A ∪ (B ∩ C) (A ∪ B) ∩ C (A ∪ B) ∩ (A ∪ C) Which of these sets are equal? A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = (A ∪ B) ∩ C(b) Find A ∩ (B ∪ C),(A ∩ B) ∪ C,and (A ∩ B) ∪ (A ∩ C).(Enter your answer in set-roster notation.) A ∩ (B ∪ C) (A ∩ B) ∪ C (A ∩ B) ∪ (A ∩ C) Which of these sets are equal? (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = (A ∩ B) ∪ C A ∩ (B ∪ C) = (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) c) Find (A − B) − Cand A − (B − C).(Enter your answer in set-roster notation.) (A − B) − C A − (B − C) Are these sets equal? Yes No

Q: Prove: If A,B and C are sets, then A ×(B ∪C) = (A ×B)∪(A ×C).

A:

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and C = {a, b, c, d}. What is |A × C|?

A: Given that A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and C = {a, b, c, d}.  We have to find |A × C|.

Q: Let A= {1, 2, 3, 4, 5} and B = {∅}. Find A ∪ B.

A:

Q: Use the given sets to find (A∪B)∩C   A={1,2,3,4,5,6,7,8} b={2,4,6,8,10,12} c={3,5,7,9,13,15}

A: Given that, A={1,2,3,4,5,6,7,8} b={2,4,6,8,10,12} c={3,5,7,9,13,15}

Q: Say True or False and justify your answer. P(A∪B)⊆P(A)∪P(B)

A:

Q: If A={1,3,5,7,9,11}, B={2,4,6,8,10}, and C={2,3,5,8}, then what is ((A∪C)∩B)∪(A∩C)?

A: Given setsA:{1,3,5,7,9,11|B: {2,4,6,8,10}C: {2,3,5,8|

Q: If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, find the following. (Enter your answers as a…

A:

Q: Find the set (A∪B)∩C if A={0},B={1,2} and C={−1,0,1,2}

A:

Q: Find |AI, IBI, AB, and IABI. -2 A 1 2 ] B = [2 -2] 4-2

A: a) A=(-2)(-2)-(1)(4)          =4-4           =0⇒|A|=0b) B=(2)(-2)-(4)(0)           =-4-0…

Q: U = {1, 2, {1}, {2}, {1, 2}}      A = {1, 2, {1}}       B = {{1}, {1, 2}}       C = {2, {1}, {2}}.…

A:

Q: Find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if the sets…

A: We have to find the number of elements in A1 ∪ A2 ∪ A3 if there are 135 elements in each set and if…

Q: A  =  {E2, E4} B  =  {E1, E3} C  =  {E1, E4, E5} P*A=0.4 P*B=0.4 P*C=0.6 P(A U B)=0.8 Find  AC.…

A: Solution-: Given:  A={E2,E4} B={E1,E3} C={E1,E4,E5} We want to find  (a) Ac=? (b) Cc=? (c) A∪Bc=?

Q: Use the set definitions A = {a, b} and B = {b, c} to express each set below. Use roster notation in…

A: Given,           A = {a, b} and B = {b, c}

Q: Find the sets A and B if A − B = {1, 4, 7, 11}, B − A ={2, 20}, and A ∩ B = {3, 5 ,19}

A: Set Question

Q: Let à (6, 7, 4) and 6=(3,2,2). = (a - b) × (a + b) i

A: We are given that, a→=6,7,-4, b→=3,2,2 We have to find: a→-b→×a→+b→

Q: Let A and B be sets. The symmetric difference of A and B is Select one: a. (A − B) n (B − A) - - O…

A: Given: Two sets A and B. We have to write the symmetric difference of A and B.

Q: If n(A ∪ B) = 2n(A), then A and B are equivalent sets.

A: Here use definition of equivalent set

Q: Let A = {3, 4, 5, 6, 9}, Write down each of the following sets. (a) An B. (b) {b-2: be B and b+ 2 &…

A:

Q: Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B.

A: A ∪ B = {2,4,6,8} ∪ {6,8,10,12}

Q: Let A = {1, 3, 5, 7, 9},  B = {3, 6, 9}, and  C = {2, 4, 6, 8}. (d) A ∩ C:  (e) A − B:  (f) B − A

A:

Q: Find the sets A and B if A − B = {1, 5, 7, 8}, B − A = {2, 10}, and A ∩ B = {3, 6, 9}.

A:

Q: Let A = {1, 5, 9} and B = {1, 2, 4, 7}. Determine the set A × B

A: Given that Let A = {1, 5, 9} and B = {1, 2, 4, 7}. To determine Determine the set A × B

Q: Let A = {-9, -7, -6, -4, -3, 1, 3, 4, 8, 10} and B = {-7, -6, -4, 1, 4, 8, 10}. How many sets of C…

A: Given that C has a property thatfrom the second condition we can conclude that all the elements of B…

Q: Let A and B be sets. The symmetric difference of A and B is Select one: a. (A − B) n (B − A) O b.…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.