2. Let A = {1,3, 4, 6, 9}, B = {r | zEN and z < 5}, C = {x|a is an integer that can be wholly divided by 4, and1 7} and U = N. List elements of the following sets. (a) AnB (b) Anc (c) AUC (d) A D (e) (AUC)nD

Q: 5) now that for all n EN, if A1,A2, ..., A and B are any sets, then n 11 nc₁x) = (N₁) va (A₁\B) B.…

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: (b). We consider the example of a set which is not a nbd. of any of its points.

Q: c. Which set is equal to (B\A)¢? d. What is the cardinality of a countably infinite set?

A:

Q: 5. Suppose that A is a set and {Bn}nɛI is an indexed family of sets. Prove that A - UB, = N(A – B„).…

A: I have given the proof using the properties of sets

Q: For the given set A, determine whether P is a partition of A. A = R ("All Real Numbers"), P =…

A: Here, A= R ("All Real Numbers") P={C" sub "y: y is an element of R and y &gt; 0}, where C" sub "y =…

Q: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: Suppose X is a set with 84 elements that is partitioned into four subsets: X1, X2, X3, and X4. If X1…

A: Given total number of elements = 84 Let  number of elements in X4 be a As X1 has twice as many…

Q: 2. Use the set builder notation to give a description of each of the following sets: 1 2 3 4 5 2'3'…

A: Given

Q: . Is it true that the null set is a subset of every other set? (Y/N)

A: If a set has no element then the set is called null set. Null set is also called empty set. It is…

Q: 12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose…

A: Given B⊂A. A=n and B=k Now if any subset C of A has 3 elements in intersection with B then C≥3 For…

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: Suppose that A = (3, 7,1 6}, B = (3, 16}, C= (7, 16}, and D = {7,8, 1 6}. Determine which of these…

A: Set A is said to be a subset of Set B if all the elements of Set A are also present in Set B. In…

Q: 3. List all the entries of the following sets: a) A = {a la € Z+ and -11 < a ≤ 11} b) B = {b | b =…

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:

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

A:

Q: Suppose that A = {3, 7,1 6}, B = {3, 16}, C = {7, 16}, and D = {7 ,8, 1 6}. Determine which of…

A: Subset :  A set P is a subset of a set Q if all elements of P are also elements of Q , Q  is then a…

Q: Identify the type of set (finite, infinite or empty) as described by the following: 1. A = {stars in…

A: A set is said to be finite if it contains only finite number of elements. A set is said to be…

Q: 2.4.6. Show by example that it is possible for the union of infinitely many closed sets to be open,…

A: Let Fn be a closed set

Q: 3. Find the number of elements in A, UA,UA, if there are 100 elements in each set if a) the sets are…

A: Since you have posted multiple subparts we solve first three subparts for you To get the solution of…

Q: 1. Let A and B be two finite sets such that n(A) - 20, n(B) - 28 and n(A u B) 36, find n(A n B). а.…

A: As per guidelines we are going to solve one question

Q: Which of the following are disjoint sets? O B.(1,2,8) and (2,8,4) O C (1,2,5) and (3,4,5) (1,8,5)…

A: Given the sets:  1,2,3 and 2,3,4 1,2,5 and 3,4,5 1,3,5 and 1,3,6 1,3,5 and 2,4,6 We have to check…

Q: Which of the following pairs of sets is a disjoint set? O (1,2,3,4) and (x x is a natural number and…

A:

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: [2.28] Which of the following sets are convex and which are not? a. {(x₁, x₂) x² + x² ≥ 3}. : b.…

A:

Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: 2. If A = {a, b, c}, B = {1,2, 3}, C = {r}, and D = 0, list all of the elements in each of the…

A: Cartesian product of sets

Q: 17. Which of the following accurately defines the complement of a given set, say A? A. {x|x€U and…

A: Complement of any given set is defined by all the elements in the universal set U which do not…

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

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: The cardinality of x = {n|1<n s 96, n is not divisible by either 2, 4 or 6} is

A:

Q: (b) How many minimal elements are there in the ordered set (X,|), for X = {4k + 2: k > 2}? Let us…

A: Given the poset ordered set X,| for X=4k+2:k≥2. To find minimal elements, we must find a∈X such that…

Q: Consider the sets A = {x € Z*, x < 13 | x prime} B = {x e Z*,x < 13 | x even} C = {x € Z*,x < 13 |…

A: We know that the set of positive integers is written as . We have to find the size of the set  .…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set A × B = {(a, b) : a E…

A:

Q: Which of the following is NOT a finite set? * O A set of vowels. O {x:xE N, 1<x < 5} O (x:xe Z} O A…

A:

Q: Let A = {a,b,c,d} be the set containing the four elements a, b, c and d. Let S = {X |X is a subset…

A: Sets

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: 2. If A = {a,b,c}, B = {1,2,3}, C = {x}, and D = 0, list all of the elements in each of the…

A: We have to find Cartesian product of part (c) and part (d)

Q: 3. Is the set of all brown dogs a subset of the set of all dogs? Why or why not? 4. Is the set of…

A: We need to find the solutions to the given 3 problems. Let's begin.

Q: 2. Determine if the following statements are true or false. Here A represents any set. (a) ¢ C A (b)…

A: Used simple logic to prove.

Q: a) A' - B' is equal to...   b) If A = ∅ then total number of elements in P(A) are ...   c) A set…

A: The set X-Y contains all the elements that are present in X but not in Y. The set X' is the…

Q: 2. (i) Show that given finitely many countable sets A1, A2,, An, the set A1 x A2 x .. x An is also…

A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

Q: 1. List the elements of each of the following sets using roster notation: a. {x € Z* |- 5 <x< 5} b.…

A:

Q: Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly…

A: Given, A is a set with 7 elements In a set the order doesnot matter so here we use combinations.

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

Q: Which of the following is the correct representation of A = (2,4.8.16.32. in set builder notation? A…

A:

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: 2.3 Show that the following sets don't satisfy the law of contradiction and the law of excluded…

A: part(a) GIVEN μAx=11+x TO SHOW: given function don't satisfy the following laws 1) law of…

Q: 4. Suppose you wanted ; –) and :0 to be the elements of a set S. (a) How could you indicate this? In…

A: We want ;-) and :o to be the elements of a set S.