1) For the universal set U and the given sets U = {1,2,3,4,5,6,7,8,9,10}, A= {1,3,5},B = {1,2},C = {2,5}, verify that the following identities hold by calculating each side of the equation separately. a) (AUB) = A OB b) (AUB)n(AUC) = AU(BnC)

Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

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Q: Prove that for any sets A, B, C: (AUB)-B A - B

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Q: LAUBUC = ANĒNT. %3D

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Q: Show that the sets [0,1] and (0, 1) are equinumerous 7.

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Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 10}.  (Enter your answers as a…

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Q: 3. Let A and B be two sets. Use set operation properties to prove the identity ,AÐB = AUBU (AO B).

A: To prove the identity

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (C n D) = D where Ce…

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Q: C) = (*,') + "- ), Give an interpretation involving subsets. Problem 4) Prove that

A: See the hand written

Q: AAB = (A\ B) U (B\ A). Prove or disprove: (1) (2) (AAB) (AAB)° (AUB) \ (ANB) A¢AB° %3|

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Q: For all sets A , B and C A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C )

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Q: Consider S to be the universal set. Let X = (AUB) nC and Y = (AnT)U (An B). %3D Write out the…

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Q: Prove that for any sets A, B, C, ANB = AN C and AUB= AUC if and only if B = C. %3D Prove that for…

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Q: 2. Given A, B, and C are non-collinear points, draw the following or explain why it is impossible…

A: We have given three points A,B,C  which are non colinear  that  is these three points does not lie…

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…

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Q: 2. Prove that if A, B,C are sets such that ANBNC = 0, then (A\B)n(C\B) = AnC. Prove that for onu got

A: Recall that, set A\B means a set of elements of A that does not belong to B.

Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

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Q: Let X = {a, b, c, d,e} and let T = {X, ø, {a}, {a,d}, {a,e}}, then * %3D (X, T) is not Hausdorff but…

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Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Given the universal set U = {a, b, c, d, e, f, g, h, i, j), A = (b, c, d, j}, B (b, c, h, i), and C…

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Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: 4. Let A and B be sets, prove that P(A)UP(B) C P(AUB).

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Q: Let C, D be subsets of a set U. By proving two inclusions, show that (Cºn D) U (C N D) = D where CC…

A: Identities of the sets

Q: Show every possible 1-1 correspondence between the following sets. {A,B} and {a,b}

A: The solution are next step is

Q: given: set A = {a,b,c,d} into set B = {1,2,3,4}. which set of ordered pairs represent a bijection?

A: Consider the set S={(a,1), (b,2), (c,3), (d,4)} Here each element of A has exactly one image in B…

Q: Find the complement of the set given that  U = {x | x  I and −3 ≤ x ≤ 7}.  (Enter your answers as a…

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Q: Let C, D be subsets of a set U. By proving two inclusions, show that (C° n D) U (Cn D)= D where Ce…

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Q: Find the intersection of the sets. {r, e, a, l}∩{l, e, a, r}

A: Given:A=r,e,a,lB= l,e,a,rIntersection set:The set containing all elements of A that also belong to…

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: Determine whether or not the set {(2, 21, 0), (1, 2, 5), (7, 21, 5)} islinearly independent over R.

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Q: For the universal set U {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,…

A: Solution:     U – { a, b, c, d, e, f, g, h, i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x , y, z }…

Q: Prove the following statements about sets A and B. (AUB)° = A° Bº

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Q: Let X = (6,7), and d be the ususal mortric, d(r, y) = |r - yl Gire ezample of a set ACX, to be not…

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Q: show that empty set, X is an element of S intersection T in topology

A: Here We have to show that empty set must be in S∩T where S and T are topology on set X.

Q: Set C and the universal set U are defined as follows. U={p,q,r,x,y,z} C={p,q,x}

A: Given,        Set C and the iniversal set U are defined as follows :         U=p,q,r,x,y,z…

Q: For all sets A and B,  (A ∪ Bc) − B = (A − B) ∪ Bc. An algebraic proof for the statement should cite…

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Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

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Q: Let A and B be sets. Prove or disprove that B – A = BU (AnB)

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Q: Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show…

A: Here, {p1,p2,p3} is an affinely independent set. So, {p1,p2,p3} are linearly independent.

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: 1. Prove or Disprove: For all sets A and B, MUB- M+ B

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Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

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Q: ---A 2 Let aj 1 and ag -10 The set {a1, az, ag} will span R unless h

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Q: Let A, B, C be arbitrary finite sets from the same universal set U. - (a) Is it true that A - B C (A…

A: SOLUTION-

Q: Let X = {a, b, c, d,e} and let T= { X, Ø, {a}, {a,d}, {a,e} }, then * O (X,T) is Hausdorff and…

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Q: Prove (((LOM)-N) U(N-(LUM))) < (LU (MUN)) L, M, N are sets.

A: To prove: L∩M-N∪N-L∪M⊂L∪M∪N

Q: Prove that S UT = SN T for all sets S and T using the rules for complements of sets.

A: rules of complements x∈A⇔x∉A¯

Q: What is the size of the symmetric difference of two finite sets A and B, that is AA BI ? o IIAI -…

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