It it a subset? Let C denote the set of all house cats. 1) Ø C C is True False 2) How many cats does Ø have? No cats! О cats! Let E = {{1,2}} and let F = {Ø, E}. 1) How many elements does E contain? 2) How many elements does F have? 3) Is E E F true? Yes, it is true. No, it is false. Neither, it is undefined.

Q: 5. For the set C = {4, 5, 6, ....} is it true or %3D false that 7 e C? True False

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

Q: 4. Prove that, for any sets A and B, it is true that A C B iff AnB = A. Hint. There are two…

A: The intersection is a set operation. The intersection of finite number sets consists of elements…

Q: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

Q: Consider set A = {2,3,6} and relation R = {(2,2), (3,3), (6,6), (2,6), (6,2), (3,6), (6,3)}. Which…

A:

Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

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

A:

Q: Which of these sets are equal: {x, 1, z}, {z, 1, z, x}, {1, x, 1, z}, {1, z, x, 1}?

A: Given sets are x,1,z , z,1,z,x , 1,x,1,z , 1,z,x,1 find out which sets are equal

Q: 5. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser…

A: We used the concept that if a set contains n elements then it power set contains 2n elements .

Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

Q: Let Aand B be non-empty sets such that |A|>|B|.If the number of elements in A∪Bis atmost 42 and at…

A: Let the number of elements in A is a , hence, |A|=a . Let the number of elements in B is b , hence,…

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

A:

Q: Prove that if A and B En and Ac B, then

A:

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: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: 2. Prove that if A, B,C are sets such that ANBNC = 0, then (A\B)n(C\B) = AnC. Prove that for onu got

A: Recall that, set A\B means a set of elements of A that does not belong to B.

Q: (2) (a) Show using set identities that AUBU (AOBOT) = AUBUT (b) Prove by contradiction that if A C…

A:

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: The number of non-empty subsets of B is |{S:SC A, S = 3 and Sn B = 0}| = max {|S|: SC AUB, SNA| is…

A: Given that A and B are finite sets satisfying A=6, B=7, A∩B=2. Since, B=7. So, total number of…

Q: SUppose K,n EZ and O < Kcn. Prove +hat by (onsi nsi dering subsets of (1,... --- --- (^) - (":') + (…

A: The given problem is to prove the following identity using the basic mathematical identities.

Q: find fundamental set of soleubions cwith d real va lues for

A: Using differential equations,

Q: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

Q: 2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

A:

Q: The symmetric difference of sets A and B, consists of those elements which belong to A or B but not…

A:

Q: One of the following statements is true: A) Archimedean property say that if y > 0, x € R, then…

A: Archimedean property named after the mathematician Archimedes. The set of real numbers ℝ has the…

Q: 2) het A, B and non- dijoint diagranı be Three Cveyla Ony using sets von Show (B-C)Ule- A) # A-8

A: firstly, we will draw all given set region then we comparing both side

Q: 3. For the set C = {4, 5, 6, ..} is it true or false that 4 E C? True False

A: We have to check

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Consider that  the set S has 7 elements. The subsets can have 3 elements, 2 elements, 1 element, and…

Q: 1 A class of 40 students was each required having three textbooks in each of Economics, Mathematics.…

A: Topic:- ven diagram

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…

Q: 2) Explain how you count the number of elements in the set A = {n EN| n <500 and gcd (n, M) = 1},…

A:

Q: (3) Let S = {; Find with prove :m eN,n E N}. %3D suprenum of S. (4) What is an unbounded set?

A:

Q: 2. If the set S in each part is finite, write down S. i. S={primes) ii. S= (even primes) iii. S=…

A: 2. Given that S in each part is finite . i. S={Primes}. S={2,3,5...}. This set has infinitely many…

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Let S(a, b) = {na + mb : n, m ∈ Z}. For any a and b in Z, not both zero, the set S(a,b) is precisely…

A: Take the set S={ax+by&gt;0:x,y∈Z} Without loss of generality, assume that a&lt;b. Then b−a&gt;0 is…

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: 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: 2) Let mf lu and (a,m)=| a,bE Z such that Let h= Om ( a) show and and (h,m)=1, %3D let. ne OmCab)…

A:

Q: 22. Let 2 be a non-empty set and let C be all one point subsets. Show that o (C) = {A C 2 : A is…

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: (4.1) For sets A and B. prove that P(AB) = P(A)~P(B).

A:

Q: prove that (1, 6) 13 an o pen set 13 an open çet.

A:

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

A:

Q: 4. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

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: The symmetric difference of two sets A O B is the set of elements that are in either the set A, or…

A: The aim is to show that, A⊕(B⊕C)=(A⊕B)⊕C It is known that, A⊕B=A∪B-A∩B So A⊕(B⊕C) can be written as,…

Q: Let S = {a, b,f,g, i, k, m, q, t} . (1) How many subset of S have exactly 3 elements? (2) How many…

A: We have to find no. Of subset as per given question.