Q1:A) Let X = R and r be the usual topology on R.If Y-[4,6). 1) Determine the open ,closed ,open and closed for the following sets: (4,5), (4}. (5,6]. 2) Find 31

Q: Which of the following sets is not closed for the operation °, which is defined by the rule a°b = a…

A: The objective of this question is to determine which set of integers is not closed under the…

Q: 6. How many mappings are there from A to B where A={1, 2, 3, 4} and B = {Low, Middle, High}. How…

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Q: List the ordered pairs in the relation R from A ={0,1,2,3} to B = {0,1,2,3} where (a,b) ϵ R, if and…

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Q: b) Let A = {0, 1, 3,4, 5, 6} and define the relation R and S on A as follows: For every (x, y) €A,…

A: all the ordered pairs (x,y) in the relation R and S and SoR are given below...

Q: Define two relations R1 and R2 on set positive integers. R, = {(a,b)|a > b} and R2= {(a,b)|a? = b }.…

A: Composition of relation

Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

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Q: 4. For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10}…

A: We have to check the given sets are equipollent or not.

Q: Which of the following sets spans R³? {(0,1,-1)} None of these O {(0,1,-1).(0,0,0)} O…

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Q: Use any method you choose to shc are sets.

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Q: Let A:= {2} and B:= {2,3,5}. Give the Cartesian product of sets A and B, furthermore the power set P…

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Q: For the four pairs of sets below, determine whether or not they are equipollent. i.) {2, 5, 10} and…

A: We have to find the equipollnt sets from the given pair of four sets.

Q: In this task there are two situations: one dealing with counting toothpicks and the other dealing…

A: We need to justify the nature of the relationships among the data points whether it is discrete or…

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: . Given the relation R1 from X = {1,2,3,4} to Y = {a,b,c} and R2 from Y = {a,b,c} and Z = {6,7,8}…

A: Here given  Relation R1 from X=1, 2, 3, 4 to Y=a, b, c is defined as R1=1, a, 2, a, 2, b, 3, c, 4,…

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} %D are two sets. find R = {(x, y): x EX and * y EY and…

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Q: Which of the following are difference sets? (ii) {0, 1, 3, 5} in Z13,

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Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

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Q: Differentiate the sets (0) and 0.

A: We need to differentiate between the sets φ and φ. Note that φ is a set containing and element which…

Q: 1. Use set identities to show that (A U B) n (B U A) = A where A and B are sets. Let A = {1,2, 3}…

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Q: Let A = {1,2,3} and B = {1,2,3, 4}. The relations R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2),…

A: Given that  R1={(1,1),(2,2),(3,3)}R2={(1,1),(1,2),(1,3),(1,4)} We need to find  a. R1∪R2b. R1∩R2c.…

Q: Which of the following sets spans R°? None of these {(-3,0,2)} O {(-3,0,2),(5,1,0),(0,1,1)}…

A: The solution is given as

Q: Let A = {0, 1, 2} and let B = {-2, 0, 1, 2}. %3D

A: Given,        A=0, 1, 2, and B=-2, 0, 1, 2

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

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