Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Finda) A ∩ B ∩ C. b) A ∪ B ∪ C.c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.

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Q: If a set A has 63 proper subsets, what is |Al? 6. 7 8. 9

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A: We will transform this logical statement into descriptive statement into next step.

Q: Prove that if A ⊂ B and B ⊂ C, then A ⊂ C

A: Given problem is :   Prove that if A ⊂ B and B ⊂ C, then A ⊂ C.

Q: Let A = { a, e, i, o, u} and B = { a, b, c, d}. Is A a subset of B ? No.(Why?). Is B a subset of A?…

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Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: Write the proof. Using information from the diagram to prove that A ABD A CDB . Statements Reasons

A: Solution: The objective is to prove ∆ABD≅∆CDB

Q: o sets are equal if and only if A=B b. ACB and BCA c. AcB and BCA d. ACB and BCA а.

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Q: 4. Use set identities or different proof method to show that: (A U B) n (B U A°) = B

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Q: Given Universal Set = { a,b,c,d,e,f,g,h,i,j}; A = { a,b,c,e,g,h}; B = { b,c,e,f,h,i}; C = {…

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Q: Consider selecting two elements, a and , from the set A (a,, c d.e). Lt al possible bts of A using…

A: " Since you have posted a two questions, we will solve first question for you. To get another…

Q: Given the premise set Γ={p,q,r,s} and ϕ=(p∨q)∧r, which of the following are the essential premise…

A: Answer : { p , r } and { q , r }

Q: Given the universal set U ={0, 1, 2, 3, 4, 5, 6, 7, 8) and sets A = {0, 2, 4, 6, 8}, B = (1, 3, 5,…

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

A:

Q: 1. Let A, B, and C be sets. Given A C B, show that (a) AnC C BnC. (b) ВС А.

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Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

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

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Q: According to Bayes' Theorem, letting p = P(A), q = P(B), r = P(A|B), we can express P(B|A) as...…

A: Given that P(A) = p P(B) = q P(A | B) = r

Q: Create a Venn diagram that shows the following elements: • a, b,c, d in set A • x, y, z in set B •…

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Q: Prove that if a|b and b|c, then a|c.

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Q: I, For A and B of Hhe univer sal ß subsets proside a in terse ct B set X, provide a formal prof for:…

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Q: Suppose proposition g is TRUE and propostion d is FALSE. Select all the TRUE statements. OgA ¬d OdAg…

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Q: Let A = {raisin, prune, lemon, pear}, B = {lime, cantaloupe, orange}, and C = {lemon, berry, peach,…

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Q: 12. Prove: If AC B and C C D, then ANCCBND.

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Q: 1. Prove that, if A, B, and C are sets and if ACB and ACC, then ACBOC.

A: To prove: A⊆B∩C

Q: Let A be a 7*4 matrie. What must a and b in or der to TO= Ax?

A: For it to be possible that two matrices A,B  can be multiplied as AB then we must have number of…

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Q: If A is a subset of B, and B is a subset of A, then does A=B?(Y/N) If A maps onto B, and if B maps…

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Q: If a, b, c are in A.P., then prove that ao +C), b(c +a), c(a + b) ab are also in A.P. bc са

A: arithmatic sequence prove , a, b,c are in A.P then prove

Q: Let A, B and C be any three sets. Then Ax (BUC)=

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; wheren is total number of distinct…

A: Consider two sets A and B. Then the union of these two sets contain all the elements in both A and…

Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

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Q: Given the sets A={1,2,3,4,5), B={2,3,7,8}, C=(1,9): (a) Compute C\(AUB) (b) Is it true that (Bn C) C…

A: Given that,

Q: Which set of given information does not prove ACAM ACOM? O ZMCA EZMCO, ZCAM2 ZCOM O AC OC, ZACM E…

A: Given

Q: 2. If sets A and B are not regular, is ¬A regular? Is A B regular?

A: In this question given that A and B are not regular set We need to find A∪B is regular

Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

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Q: Given: sets R and S are transitive. True/False: RNSis transitive O True O False

A:

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: 1. If A ana B are sets, show that Ac B if and only if An B = A.

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

Q: How to solve this?

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Q: Let A = {c, d, f, g), B = {f, j}, and C = (d, g}. CsA A) True (B) False

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Q: Show that if A and B sets then A – B = ANB

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Q: Use the Venn diagram below showing the number of elements in regions I through IV to determine the…

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Q: In drawing 3 CD’s from a lot, defective and non defective CD’s , let A, B , C and D mean at least…

A: let A, B , C and D mean at least one Defective CD, at least one non defective CD, 2 defective CD’s…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.