Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if sup(B) exists O b. the set An B is bounded O c. the set A is bounded O d. sup(A) s sup (A U B)

Q: Let {E} be a countable collection of sets of real numbers. Then UEn ≤Σm* (En) n * m n

A: Definition of outer measure: The outer measure of a set E is defined as, m*(E)=inf∑j=1∞Qj, where…

Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Let A, B sets such that A ¢ B and B C C. Prove that A ¢ C.

A:

Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

A:

Q: Using contradiction method, prove that for every nonempty sets A and B, An (B- A)=0.

A: The given problem is to prove the following set identity using the contradiction method.

Q: Find an example of nonempty, distinct sets A, B, C for which (ANB) UC = (AUB) nC.

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: Let A and B be sets. Prove that A c B if and only if A NB = A.

A:

Q: Let A be a bounded non-empty set. Then inf A < sup A. True False

A:

Q: Let A and B be nonempty sets of real numbers. If sup A exists then: Choose the correct option: a.…

A: Sup(A) denote  least upper bound of set A

Q: Suppose A and B are finite sets. Prove or disprove: (aun-aun)- (AUB) = (A u B) ) + Dsjnt(A, B)

A: Consider the equation

Q: Let B and C be the subsets of some universal set X then prove that (C N B')' = BU C'

A:

Q: Let (Un) be a sequence of open sets in R then a) U₁is open, b) nis open.

A:

Q: Let A and B be two measurable sets prove that if ASB then BIA is measurable and m(B\A)=m(B)-m(A)

A: The given problem is related with measure theory. Given that A and B are two measurable sets.  We…

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

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B)n (AUC)

A: To prove:- Prove that for any sets A, B, C we have AU (B∩C) = (AUB)  ∩(AUC) Method :- I use venn…

Q: B. Let B and C be the subsets of some universal set X, then prove that (C – B)' = BU C'

A: let B and C be the subsets of some universet x1 then prove that (c-B)' = BUC'

Q: Q.Prove If ANB is pathwise connected set, then A andB are or disprove the following: pathwise…

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: Let A be a subset of Real numbers. Prove that A is Open iff  A Compliment (A') is a closed set.

A:

Q: Let A, B be non-empty bounded sets, and A Ç B (A is a proper subset of B). Then sup A < sup B. True…

A: Let A=(1,2] and B=[1,2]

Q: 1. Let A and B be sets. Prove that A C B if and only if An B=A

A: Prove that A⊂B if and only it A∩B

Q: prove that i } X is a Coun table set and P: X>Y is asurjecbive then Y is Countable

A: Note: X denotes cardinality of X, that is number of elements in the set X. If X is countable means…

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 and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A: a)If sup A and sup B exists then          supA∪B=max{sup A,sup B} So supA∪B exists. First option is…

Q: Let A and B be finite sets such that B = {b1, b2}. Prove that |A – B| < |A|.

A: We are given that A and B are two finite sets, where B= {b1, b2}.We have, |B| = 2, and let |A| =…

Q: Let A and B be sets. Prove that Ac B if and only if AnB = A.

A:

Q: Both P and Q are transitive relations on set X. Proof that a. Pn Q is also transitive b. PoQ is also…

A: Given,    Both P and Q are transitive relation on set X.

Q: Let U= set of all natural numbers A = {r:x = 7y, y E N}, B = {r:x = 4k, k E N}, and C = {r:x = 3n +…

A:

Q: Find sets A, B and C such that A ∩ B,    B ∩ C and A ∩ C are non-emptysets and A ∩ B ∩ C = φ.

A:

Q: If C {x: x2 + 11x + 30 0, x e N}, then C is a/an? %3D Infinite set Finite set None of these Empty…

A: We have to find the set C

Q: Let A and Bbe finite sets satisfying |A|= 9, B| = 6 and |An B = 2. Calculate the following: () |AUB…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

A:

Q: 4. Let A and B be any two non-empty sets. Prove that P(ANB) = P(A)NP(B).

A:

Q: Prove that, for any sets A and B, it is true that A ⊆ B iff A ∩ B = A.

A: Use the following definitions, to obtain the solution. Let A and B be any two sets. The…

Q: Let A be an uncountable set and let B be the set of real numbers that divides A into two uncountable…

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

A:

Q: T have to show rigorous proof of the inclus (An B) x C c (Ax C)UCBXC) 1,B.and C, Sets non-em pty of…

A:

Q: 3. Let a, b e R such that a < b. Prove that the open interval (a, b) is an open set in R.

A:

Q: supC = supA × supB.

A: This is a question from real analysis with usual topology.

Q: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf B ≤…

A:

Q: Let R (the set of real numbers) be equipped with the Euclidean topology, then A, a finite subset of…

A: Solution-

Q: Suppose S and T are sets of real numbers. Prove that S is closed iff it is the complement set of…

A: Take               Then clearly S is the complement of T. To prove S is closed iff T is open.

Q: Let A be a nonempty subset of a bounded set B. Why does inf A and sup up A exist? Show that (a) inf…

A:

Q: Prove that a set A is connected iff A is and interval.

A:

Q: 2 Let A and B be two measurable setsa prove that ie BAIS measurable and mCB\A) =M CB)-mcA) %3D

A:

Q: Let A, B be sets. Prove that A ⊆ B if and only if A \ B = ∅.

A: Given A, B be the set. We have to prove that A⊆B if and only if A-B=∅. Let A⊆B Then we will prove…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.