Q1) Consider the universal set U = {1,2, 3, 4, 5, 6, 7,8, 9} and sets A = (1,2,5, 6}, = {2,5, 7},C = {1,3,5, 7,9}. Find: 1)ANB; 2)AnC; 3) A°; 4)C“ ; 5)AOB; 6)AOC; 7)AUB; 8)BUC; 9)A\B; 10)(AUC)\B .

Q: et A and B be sets. Show that if AUB=U, then ACB. (Note: U is the universal set.)

A: A universal set (usually denoted by U) is a set which has elements of all the related sets, without…

Q: The set of all directed line segments that are equivalent to a given directed line segment PQ\is…

A: The set of all directed line segments that are equivalent to a given directed line segment PQ \ is a…

Q: Let v be represented by the directed line segment from (0, 0) to (3, 2), and let u be represented by…

A: Given that, v is a line segment from (0, 0) to (3, 2) So, v=(3,2) - (0,0)= (3,2)   Given that, u is…

Q: Complete the proof: If A≤B and B≤C, then ACCn(transitive property for set in inclusion) Need to…

A:

Q: Given the relation R = {(u,t),(v,t),(w,t),(w,u),(w,v)} on a set A = {t,u,v,w}, what is/are the…

A: topic - relation

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

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Q: Consider set A = {2,3,6} and relation R = {(2,2), (3,3), (6,6), (2,6), (6,2), (3,6), (6,3)}. Which…

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Q: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

A: Consider the sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is not…

Q: Which of these sets are equal: {x, 1, z}, {z, 1, z, x}, {1, x, 1, z}, {1, z, x, 1}?

A: Given sets are x,1,z , z,1,z,x , 1,x,1,z , 1,z,x,1 find out which sets are equal

Q: Find the dimension of the set S= {(2, 4), (4, 8)}?

A: The dimension of the set S can be find out by finding the linearly independent vectors in it.…

Q: => find fundamental set of Se yo=-3x²e-3x ZR 7:

A: We have to find the fundamental set of solution.

Q: Express (4, 10) as a set {x : |x – al < c} for suitable a and c.

A:

Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

A:

Q: Determine whether is a linearly independent set of vec- 3 11 tors in R3.

A: A set of vectors v1,v2,v3,…,vk in a vector space is said to be linearly independent if…

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

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Q: Let १ १G,१ी, (३,5) , (3 ), (4,2 ), ( 3 4) 5 %3D and 4. १,०) (2) (৬,), (,০), (3,) 3 %3D which of the…

A: The solution of the problem is given in the next step.

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

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Q: 3) Consider the subsets [0, 1] and [3,4] of R, the set of all real numbers with the euclidean…

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Q: Let A=span(u,v) and B=span(u,v,w). Which statement is true? - A ≠ B and that is all you can say…

A: Let A=span(u,v) and B=span(u,v,w).

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

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Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

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 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: State whether each of the following statement is true or false. Justify your answer.(i) { 2, 3, 4, 5…

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Q: find fundamental set of soleubions cwith d real va lues for

A: Using differential equations,

Q: Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point,…

A: Axioms3 of Fano’s geometry: The axiom 3 in Fano’s geometry is stated as “not all points of the…

Q: Let X = {a, b, c, d,e} and let T = {X, Ø, {a}, {a,d}, {a,e}}, then * O (X,T) is not connected but it…

A: No information is given for topology on Y So i have solved only the middle question

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: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: U is the set of TV owners and W is the set of people who watch The Walking Dead, describe W' in…

A:

Q: Let A, B, C be points in 3-space. Suppose that AB represents u and BC represents v. Then AC…

A: Given statement is true.   Because it is following triangle rule of vector addition.   According to…

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

A:

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d}, {b,c,d,e} }, then O XT) is neither…

A: Option 1 is correct.

Q: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: Let U = {m,a,t,h,e,w,d,i,n}   X = { e,w,m,a,t}              y = {e,w,d,i,n}            Z= {h,e,w}…

A: U = {m, a, t, h, e, w, d, i, n}   U= Universal set X = {e, w, m, a, t}              Y = {e, w, d, i,…

Q: Prove using Venn diagram that An (B U C) = (A n B) U (A n C)

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Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r…

A: The given set is S=1,1,1,2,2,1,3,2,3,3. We know that the polytope:…

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: EX LeT X = {!,2,3,415,6} T- Ex,¢,てり,E4,しろ4), [ス456 Topology.?

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Q: Express (4, 10) as a set {x: Ix - al&lt; c} for suitable a and c.

A:

Q: Is it true that (A×A)∖(B×B)=(A∖B)×(A∖B) for any two sets A, B? If it is true, prove it. Otherwise,…

A: Explanation of the answer is as follows

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: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

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Q: 2 Find values for a, b, and c such that is an orthogonal set.

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

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.