Let 4, B, and C be sets. Show that a) (A - B) – CSA C. b) (A - C) n (C- B) = 0.

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: ) (AO B) © (A^ B) = A UB.

A: Introduction :

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: 2. Classify each set as closed, open, or neither. Justify your answer. A= {-+:nEN} E. 1-:] [0, 1)

A:

Q: For all sets A, B, and C, it holds that (An C) U (B \ C) = (B U C) \ (C \ A). True False

A: We have solve the set true and false

Q: Let A and B be two sets with a finite number of elements. Show that the number of elements in An B…

A: Given A and B are two finite sets. To show that the number of elements in A∩B plus the number of…

Q: A set D C RP is disconnected if and only if D = EU F, where E, F are non-empty and EnF= ø,EnF = Ø.

A:

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

A:

Q: Determine whether the symmetric difference is associative; that is, if A, B, and C are sets, does it…

A: Truth table for the symmetric difference is,

Q: Let A, B, and C be non-empty sets. Then Cx BxA=C×A×B if and only if O A=B O A=B=C O None of these O…

A: We can tackle this problem easily by assuming some examples  case (i) Let A=B=C = {1,2} we have,…

Q: Q.A. Is the nonnepatbe orthaut t. a cohvek set?

A: Answer is negative

Q: Disprove the following statement by finding a counterexample. For all sets A, B, and 6, C, An (BUC)…

A:

Q: Create three non-empty sets A, B, C, that show this statement is FALSE: For all sets A, B, C: A- (Bn…

A:

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

A: Let A, B and C are sets. We have to find out that A-B = A- C implies B = C or not If not then we…

Q: Show that if A, B, and C are sets, then|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| +…

A:

Q: 2. Let A, B, and C be sets. with (A - B)nC the empty set. Prove that AnC C B.

A: Recall the following. A-B=A∩BcIf x∈A⇒x∈B, then A⊂B

Q: Let A, B,C be three sets. Show that if BC A and C C A \ B, then BC A \ C.

A:

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: Draw figures showing two sets A and B, so that B C A. DO NOT draw the set elements.

A: As we know the meaning of B ⊆ A is that B has few or all elements equal to the set A B ⊆ A subset…

Q: 5. Write these sets in set-builder notation, where U = {1, 2, . . . , 20}. (a) {11, 12, 13, 14} %3D…

A: As per our guideline we are supposed to answer only three subpart of question you can repost other…

Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

A:

Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

A:

Q: Prove that if A and B are sets, then A - B = An BC.

A:

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

A:

Q: Can you conclude that A = B if A, B, and C are sets such thata) A ∪ C = B ∪ C? b) A ∩ C = B ∩ C?c) A…

A: According to the given information, it is required to conclude that A = B if A,B,C are sets such…

Q: Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

A: No, it is not true. EXAMPLE- Let A= {2}  B= {{2},3,4} C={{2},3,4,5,6} We can see here that,

Q: What is the union of sets A and B?

A: Assume the independent sets A and B. Set A = 0,1,2Set B = 4,5,6

Q: Give a counterexample to show that the statement For all sets A, B and C, if A⊈BandB⊈C,thenA⊈C.…

A:

Q: Suppose A, B, and C are sets, A. Prove that: Ax (Bn C) = (A × B) n (A × C) %3D Using Membership…

A:

Q: Let A, B, and C be three sets. If A⊕C=B⊕C, show that A=B

A: Solution : Given that A,B and C are three sets. And the Direct sum of set A and C is equals to…

Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…

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

A: B=C

Q: If X and Y are two sets such that X ∪ Y has 50 elements, X has 28 elements and Y has 32 elements,…

A: Given that n(X ∪ Y)= 50  n(X)= 28 and n(Y)=32  We have to find n(X ∩ Y )= ?

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

A:

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: b) The number of elements of the set A = {{{Ø}}, {{Ø}} n {Ø}, {Ø} U {Ø, {Ø}}} equals

A:

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

A:

Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

A:

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

A: Given :- A, B and C are three non empty sets. To complete the statement. C*B*A = C*A*B if and only…

Q: Let A, B be any sets with BCA. Then |P(B×B)[s|P(A×B)| O IP(AxB)|s|P(B×B)| O IP(AxB)|=|P(B×B)| O None…

A:

Q: (c) Show that the set {r EN | x² % 4 = 1} is equal to the set {EN | x² % 8 = 1}.

A: Two sets are said to be equal if the number of elements in both the sets are equal. Now, we have one…

Q: 2. Prove that by laws of set, (A - B)- (B - C) = A -B

A:

Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

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

A:

Q: Let A, B,C be three sets. Show that if BC A and CCA\B, then BC A\C.

A:

Q: If A, B, C are sets, then a. A\(BUC) = (A\ B)(A\C) b. A\(BnC) = (A\ B)U(A\C)

A: We know that for two sets A and B: A \ B = A∩Bchere Bc is the compliment of set B Distributive Laws:…

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.