12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose intersection with B has 3 elements?

Q: Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i}, C = {f, h} and U =…

A: Hey, since there are multiple questions posted, we will answer first question (1) with first three…

Q: In a mall survey, 200 consumers were asked where they did their gift shopping; Macy’s, JC Penny’s,…

A: Let us denote M=Macy's, J=JC Penny’s, S=Sear's  Given that 40 people shopped at least at two…

Q: Suppose we want to choose 5 objects, without replacement, from 16 distinct objects. (a) If the order…

A: In this question, we want to find the number of ways if the order of choice is relevant and not.…

Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

Q: Suppose we want to choose 4 objects, without replacement, from 18 distinct objects. (a) How many…

A: Permutations and combinations

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

A:

Q: If set Z has 7 elements, how many subsets does it have?

A:

Q: draw a Venn diagram for n(U) = 10, n(A')= 4, n(AUB)= 9, n(B')= 5

A:

Q: Determine whether the set S = {1, x², 3 + x²} spans P2. O S spans P2. O s does not span P2.

A: Consider the given set S. S=1,x2,3+x2 Now, make the matrix from the given set. 103000011

Q: In a group of people we have 7 football player 5 baseball player 1 who is both football player…

A: Venn diagram is diagrammatic representation of similarities and differences between two concepts .…

Q: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

Q: 2. Consider the collections C = {penny, nickel, dime, quarter} D = {penny, nickel, nickel, dime,…

A: (a) The number of elements in collection C is 4 and the number of elements in the collection D are…

Q: 26. Let I be the set of all infinite sets. Is I an element of itself?

A: Given I is the set of all infinite sets.  We check whether I is an element of itself.

Q: A study was done to determine the efficacy of three different drugs-A. B. and C-in relieving…

A:

Q: 2. Enumerate (i.e. list) the members of the following sets: a. {z |z is odd positive integer and z <…

A:

Q: If A and B are both finite sets and A has n elements and B has m elements, what’s the fewest number…

A:

Q: Given that set A has 41 elements and set B has 22 elements, determine each of the following. (a) The…

A: Set A : 41 elements  Set B : 22 elements

Q: Let X, Y subset U. Suppose that n(X)= 22, n(Y)= 20, and n(X intersect Y)= 16. How many elements are…

A: Let X,Y be subsets of U.  nX=22 , nY=20 and nX∩Y=16 It is given that nU=40. Find nX'∪Y:

Q: Suppose n(ANB) = 3, n(AUB) = 38, and n(A) = 18. Use a Venn diagram to determine n(B). n(B) = %3D

A: Given n(A∩B) = 3,  n(A∪B) = 38andn(A) = 18

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: Let A = {1, 2, 3, 4, 5}. How many subsets of A have no more than 3 elements?

A:

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

A:

Q: 6. Write down all the set-partitions P of [5] such that for every BEP, if x € B and y EB then lyx ≤…

A: Please find the answer in next step

Q: Suppose S is a set having n elements and T is a set having m elements. Which of the following claim…

A: Suppose S is set having n elements and T is a set having m elements. That is n&gt;m More precisely,…

Q: Finish labeling the number of elements in the regions in the Venn diagram shown to the right, where…

A: We will find the all values as shown below by using given information

Q: 10. A salesperson living in city A wishes to visit five cities B, C, D, E, and F. a. If the cities…

A:

Q: Consider a room with 200 people. Let X be the number of days of the year in which there are exactly…

A:

Q: Suppose there were 600 nurses graduating this year.  Assume that 400 were registered nurses (RN),…

A: The numbers of registered nurses (RN) = 400 The numbers of NOT registered nurses (NRN) = 600-400=200…

Q: List the elements of set D = { x:x є N, x is a multiple of 5} where N= {1, 2, 3, ...}.

A:

Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

Q: If a set S has n > 3 elements, how many subsets of S have less than n – 1 elements?

A: Apply the simple logic of Permutation &amp; Combination.

Q: c. Illustrate one of De Morgan's laws by shading in the region corresponding to (A U B)° on one copy…

A:

Q: 8. Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: How many seating arrangements can be formed if by seating A,B,C,D,E in a row: If A,B,C sit together…

A: Given information: As per guidelines we will only answer the first three subparts, please repost…

Q: Suppose we want to choose 5 objects, without replacement, from 17 distinct objects. (a) If the order…

A: We will the number of ways in both conditions as following.

Q: Given set A with 17 elements and set B with 7 elements. a. What is the maximum number of elements in…

A: Given set A with 17 elements and set B with 7 elements. If all the elements of set A and set B are…

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: Let A={x,y,z,1} and let B= {1,2,4}. If a set  U= (A x B) U (B x A), how many elements are there in…

A: Recall the following facts.

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: Given a set A of n elements, in how many ways can you find two set P,Q ⊆ A (not necessarily…

A: Given set of  elements we need to find number ways in which A can be written as union of two…

Q: O Question 5 B = {n|n EN and 317 Next Question

A:

Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: 5. Consider the generic Venn diagram for three sets. (a) Add one figure showing a fourth set D. (b)…

A: The generic Venn diagram is:

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: Let A=​{peach, kiwi, tomato, raisin​}, B=​{lemon, watermelon​}, and C {tomato, lemon, pear,…

A: Let A and B be two sets .         1.)  n( A∪B)=nA+n(B)-n(A∩B)         2.) n(A∪B)= n(A-B)+n(A∩B)+ n…

Q: What is the Venn diagram if: U = {x:x is a natural number less than 20} A = {y:y is an odd number…

A: Given: U = {x:x is a natural number less than 20}. A = {y:y is an odd number less than 20}. B =…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.