Suppose A and B are sets such that |A| = 2 and |B| = 3. What is |P(A x B)|?

Q: a) Does B – A = C – A imply that B = C? Justify b) Next, does A – B = A – C imply B = C? Justify c)…

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Q: Let A. B. and C be non-empty sets. Then AXBXC=C×B×A if and only if* O B=C None of these A-C A-B3DC O…

A: See solution below

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: Decide, among the following sets, which sets are subsets of one and another:A = { x : x ∈ R and x…

A: A = { x : x ∈ R and x satisfy x2– 8x + 12 = 0 } ={ x : x ∈ R and x satisfy (x-6)(x-2)= 0 }= {2,6} B…

Q: 3. Find an example of two nonempty sets A and B for which A x B = Bx A is true.

A: To find an example of two nonempty sets A and B for which AXB=BXA

Q: Give an example of each of the following (a) a set which is a nbd. of each of its points, (b) a…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Suppose that |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2. Determine the smallest that |A…

A: Given, |A| = |B| = |C| = 6 and |A ∩ B| = |A ∩ C| = |B ∩ C| = 2

Q: . Is it true that the null set is a subset of every other set? (Y/N)

A: If a set has no element then the set is called null set. Null set is also called empty set. It is…

Q: If A = {x: x |B| D. None of these {x: x 2 + 11x + 30 = 0,x E N}, then C is a/an? A. Empty set B.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

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Q: 3. List all the entries of the following sets: a) A = {a la € Z+ and -11 < a ≤ 11} b) B = {b | b =…

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Q: a) Suppose A, B and C are sets. What do you need to show to prove the following using the definition…

A: Definition : A⊂B iff (x∈A⇒x∈B)WLOG : Without Loss Of Generality.

Q: If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements andY has 15 elements ; how…

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Q: Which of the following statements is true about the three sets A.B.C defined below: A=[ – 4,4]…

A: The given three sets are: A=[-4,4]B=[-6,2]C=[-2,6] i.e. the set A consists of the elements…

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

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Q: 1. Let A and B be two finite sets such that n(A) - 20, n(B) - 28 and n(A u B) 36, find n(A n B). а.…

A: As per guidelines we are going to solve one question

Q: Which of the following are disjoint sets? O B.(1,2,8) and (2,8,4) O C (1,2,5) and (3,4,5) (1,8,5)…

A: Given the sets:  1,2,3 and 2,3,4 1,2,5 and 3,4,5 1,3,5 and 1,3,6 1,3,5 and 2,4,6 We have to check…

Q: For each of these pairs of sets, determine whether the first is a subset of the second, the second…

A: Note:  A set 'A' is said to be subset of set 'B' if all the elements of set 'A' are the elements of…

Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

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Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: Decide, among the following sets are subsets of one and another: A=(x xeRand x satisfy x² - 4x + 3 =…

A: Given sets, A=x: x∈R  and  x satisfy x2-4x+3=0B=1, 3C=1,3,5D=4,5,6

Q: Given the sets X = {x: x is an odd number less than 17}and Y= {y:y is a prime number less or equal…

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Q: The closure for set P would be the set |z-(1+i)| = 2 |z(1+i)= 3 |z- (1 + i)| < 1 None of the above…

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Q: Which of the following are disjoint sets?* B.(1,2,3) and (2,3,4) O (1,2,5) and (3,4,5) O (1,3,5) and…

A: Topic:- set theory If the two sets A and B are disjoint then they have no elements in common that is…

Q: Let A and B be sets. Then B (B – A) is equal to the above A N B

A: The Venn diagram for 2 sets can be drawn as follows.

Q: One of the following sets has the cardinality No : .a R .b .c {0,1,...,20} .d [0,1]

A: Cardinality of a set is defined by total number of elements in the set.

Q: What can you say about the sets A and B if we know that a) A ∪ B = A? b) A ∩ B = A? c) A − B = A? d)…

A: (Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable…

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Q: Consider the following sets. Suppose the variable x is an element of the set of integers. A = (x/x²…

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Q: For all sets A and B, ifA-B=0, then A = B.

A: For all sets A and B, if A-B=∅, then A=B.

Q: Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).…

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Q: Find the complement of the following sets: {x x > 5 and x E W} The set of integers greater than 4 or…

A: Complement set consists all the elements of universal set other than the elements of the set in the…

Q: the diagram for the intersection of sets A and B.

A: Basic concepts intersection of two sets- Let A and B are any two sets, then the intersection of sets…

Q: Q3 ( Let A, B and C be sets. Show that (C – A)n (A – B) = 0, without using membership tables.

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Q: TRUE (c) The union of two sets, A and B, is the set of all elements in A and B. FALSE

A: We have to say whether it is true or not " The union of two sets A and B is the set of all elements…

Q: Is this set finite or infinite? {x € R|1 < x < 2}

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Q: for any sets A and B (AUB)'=A'nB'

A: We prove that for any sets A and B (AUB)'=A'nB'.

Q: Are the following pair of sets equal? Justify your answer? A = { x:x is a letter in the word FOLLOW}…

A: Set: A set is a well-defined collection of distinct objects. Equality of Sets: If two sets A and B…

Q: 28. Which of the following sets does not have the completeness axiom? A. R {0} B. R+ C. Q {0} D. R…

A: We have to determine which sets doesn't have the completeness axiom .

Q: For the sets A = {x | x &lt;= 9, x is a natural number}, B = {2, 4, 6}, C = {3, 5, 8, 10}:a. Which…

A: Here given set A=x|x≤9, x is a natural number=1, 2, 3, 4, 5, 6, 7, 8, 9 and B = {2, 4, 6}, C = {3,…

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

Q: 4. Which of the following pairs of sets are equivalent or equal? (a) A = {x : x € N, x < 6} B = {x :…

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Q: Let A, B and C be finite sets with A C B. Suppose that B |C| =5, and that |BnC= 4. Decide whether…

A: Given: A⊂-B, |B| = |C| = 5 and | B∩C| = 4

Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B ∪ C). True or False.

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Q: Does the set span R3?

A: s=310,0-11,12-1Let v1,v2,v3 in R3 , if span(v1,v2,v3)=R3 then v1,v2,v3 are linearly independent.Rank…

Q: Let A and B be sets. Then B - (B - A) ANB is equal to the above Ā NB is equal to the above

A: Here ,we are given that A and B are two sets. We need to find  B-(B-A) : Now, Here ( B-A) represents…

Q: Decide, among the following sets are subsets of one and another: A={x:x ER and x satisfy : x - 4x +3…

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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”.