1. (i)which are not.Identify which of the following subsets of R2 are open and(a)A = (1, 3) x (1,2)(b)B = (1,3) x {1,2}(c)C = AUB(ii)Provide a sketch and a brief explanation to each of your answers.[6 Marks]Give an example of a bounded set in R2 which is not open.(iii)[2 Marks]Give an example of an open set in R2 which is not bounded.[2 Marks]

Let's give it a try. To provide precise answer, I believe further reference is necessary, but I will…

Answered: 1. (i) which are not. Identify which of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 25E: Determine whether the set S={1,x2,2+x2} spans P2.

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Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
(ii) Identify which of the following sets in R² are open and which are not. Are any of these sets bounded? (a) A (b) B == (2,4) x (1,2), [10 Marks] (2, 4) {1,2}, [10 Marks] (c) C = (2, 4) x R. [10 Marks] For full mark, provide a sketch and a brief explanation to each of your answers.
Here are some set definitions that we will refer to in the exercises of this assignment. A={ 1, 3, 5, 7,9} • B={x| (x ≥ 1) ^ (x ≤ 9) } • C= {x| (x A) ^ (x = B) } • D={x| (vy)(x*y = y)} • E= {x|(3y)(x*y=y)} For each statement below, answer whether the statement is true or false, and briefly explain why. 1. 3€ A 2. 4€ A 3. 3 € B 4. 4 € B 5. 3 € C 6. 4 € C 7. CC B 8. BCC [ S 9. DcA 10. ECD G D C A D = I can give you any inteyen and call it x. Each x I give you has a y, so that for all Values of yx*y = y x=3 x=5 X= 7 X |Y LY|XOY X: = XIXI хочу |-||-|| Te و ال 13 Fol نعاما X= | 3 Since X Y X+Y 3-1 3 3 212 313 e- for all 1 the only this this is 3 bの 6 y x.. 5-4-574 0070 5 171 2 10 72 315 23 کی Š 5 5 хса alm X Y xey 9 T -q 90 00 9 9 18 9222 time the relation is true is when is false as it would need to be true in the set members

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