If A ⊂ B, can A and B be independent under any circumstances? Explain

Q: Given A,B and C required to prove that A\(B\C)=(A\B)U(A∩B∩C)

A: Given  A, B, C are any three sets  We have to prove  A\(B\C)=(A\B)U(A∩B∩C)    Let X be unversal set…

Q: Show that if a|b then -a|b.

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Q: that Sup antl Shaw SA thut inf

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Q: A rectangle can be tessellated. True O False

A: A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there…

Q: Prove that AAB = (AU B) - (An B),

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Q: Use the definition of oubset to prove : If A,B,C are set then ((BnA) -c) U ((Bnc) -A)) CCOUA)

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Q: Let A and U = H. Then A2017U is equal to

A: The given matrix is A=-120-1 find A2=-120-1-120-1=1+0-2-201=1-401 therefore A2=1-401 similarly…

Q: State whether the following Claims are true and explain why. Claim: ∃ sets A, B, and C such that: A…

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Q: Show that if A ⊂ B, then C – B ⊂ C – A.

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Q: Prove that if ACC and A CBC C, then either A CB or BCC

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Q: Prove the A.B = B.A.

A: To prove AB = BA.

Q: If C1, C2 are connected subsets of R, then the product C, xC, is a connected subset of R?,

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Q: Prove or Disprove: Va, b, c E N, if a | bc and c| ab then b lac. (Here | denotes divides.)

A: We will disprove the given statement by giving a counter example that is we will give values for a…

Q: Prove that ABC and EDC are similar

A: In triangle ∆ABC we have given  AB=3, BC=5 and CA=4In triangle ∆EDC we have given  ED=9, DC=15 and…

Q: Prove that if A – B – D and B – C – D, then A -C– D.

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Q: Use an element argument to prove that for all sets A and B, (An B) U (AN BC) = A. %3D

A: I have proved that sets on both side are subsets of each other and ten concluded that they are equal

Q: Show that (A+CBC")- = A- A'C(B'+C"A 'C) 'C" A',

A: Given: A and B are square matrices, C is a matrix of appropriate dimension. Note that…

Q: . Let A and B be two connected subset

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Is each statement true for OA? Drag "true" or "false" below each statement. K True False 2JKA = MLA…

A: 1) KA = MA - True  As both are radius of the circle.

Q: For all intgars a, if 615a, thenbla

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Q: Prove that if A ⊂ C and A ⊆ B ⊆ C, then either A ⊂ B or B ⊂ C.

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Q: Can a set and it's Complement be both nowhere dense in R? A Ac=R-A

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Q: siven: ALMN; mLL > m2N rove: MN > TM

A: We have to prove that one side is greater than other side in given triangle.

Q: Let B= %3D it justification, 2021 B

A: We have to find

Q: you to If ZA ZD and ZC ZF, which additional statement does NOT allow conclude that AABC = ADEF?

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Q: If P(A|B) < P(A), prove that P(B|A) < P(B).

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Q: . Use a two-column proof to prove the equivalence below -(PV-Q) v (-P A-Q) = ¬P

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Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: If a and b are in R^n, is −a in span{a , b }?

A: Let a,b∈ℝn

Q: Which condition would prove ΔDEF ∼ ΔJKL?

A: Given problem is : Which condition would prove ΔDEF ∼ ΔJKL?

Q: Prove: Va,b,ce Z, if a|b and a|c then a|(b-c)

A: ab  &  ac This means that b & c are multiples of a. ⇒b=a·k  &  c=a·m     where k, m∈Z

Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

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Q: Let a, b,c € R4. Prove that c+a a+b b+c c+b a +c b+a Al

A: a,b,c∈ℝ+ab+bc+ca≥c+ac+b+a+ba+c+b+cb+a

Q: Prove that if ACB, then A-B=0.

A: This question can be solved using the concept of set theory.

Q: R.

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Q: Let X = R, and M = Ø, then span (M) =

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Q: Let A = {a, a, b, c} and B = {a, b, c}. Prove that A = B. Thus, the number of times an element is…

A: Given A={a,a,b,c} and B={a,b,c} we  have to show that A=B, for  this we will show that A⊂B and B⊂A…

Q: Let A = { c, d, f, g} B = { f, j} C= { d, g} Is C C C? True False

A: Every  set is subset  of it self Here C is subset  of C

Q: Which postulate justifies that ДНАМ~ДСОW? a. AAA С. ASA b. SSA d. SAS

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Q: Can you conclude that the figures are congruent? Write a Justification. A

A: Given: AE=DE  AB=DC  Angle ABE= Angle DCE

Q: If i and i are in R™, then –i is in span {ū, 3}. |

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Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

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Q: (а-b) a (b-c)* 3 d

A: a, b, c, d are in continued proportion Therefore, we have ab = bc = cd = k (say) c=dk, b=ck=dk2,…

Q: . Prove that is A < B and B < A, then A -

A: The relation defined in the above equation represents anti symmetry.

Q: in how many ways can the numbers 1,2,3,4,5,6,7 be arranged so that  a. 1 and 7 are adjacent? b. 1…

A: a) If 1 and 7 are adjacent then we consider 1,7 as one number.  It can be 17 or 71. 2 ways. When 1,7…

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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Q: (c) If gcd(a , 133) = gcd(b , 133) = 1, show that 133|al8 b18 %3D %3D

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