Equivalence Relations and Composition of Functions
Added on 20190926
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CDMA2103 Assignment 940715105173FACULTY OF INFORMATION TECHNOLOGY &MULTIMEDIA COMMUNICATION (FITMC)SEMESTER September 2016CDMA2103MATHEMATICS FOR INFORMATION TECHNOLOGYNAME :CHANG VERN VEINSTUDENT ID: 940715105173001IDENTITY CARD NO.: 940715105173TELEPHONE NO.: 014 – 932 9125EMAIL : changvv@oum.edu.myLEARNING CENTRE: PETALING JAYA
CDMA2103 Assignment 940715105173Question 1:Let A = { 1, 2} . Write down each of the following sets: A: P(A) and P(A).Answer : Given that the set A = {1, 2}. Then the power set of A is set of all subsets. That is P(A) = {ø , {1} , {2} , {1 , 2}. The condinality of a set is the total number of elements of the set. Hence thecordinality of P(A) is P(A) = 4B: P(P(A)) and P(P(A))Answer : From past a) we haveP(A) = {ø, {1}, {2}, {1,2}}Now, we find the power set of the power set, which is the set at all subsets of P(A).P(P(A)) = {ø ; {ø} ; {{1}}; {{2}}; {{1,2}}; {{ø}, {1}}; {{ø}, {2}}; {{ø}, {1,2}}; {{1}, {2}}; {{1}, {1,2}}; {{2}, {1,2}}; {{ø}, {1}, {2}}; {{ø},{1}, {1,2}} ; {{ø}, {2}, {1,2}}; {{1}, {2}, {1,2}}; {{ø}, {1}, {2}, {1,2}}}Hence, the total number of elements in P(P(A)) are 16,Therefore P(P(A)) = 16
CDMA2103 Assignment 940715105173Question 2: Let A= {1, 2, 3}, B = {2, 3, 4}, and R be a relation from A to B.A: List the elements of A x B and the elements of R = {(x, y)  x < y}. Writedown the domain and range of R.Answer: Given A= {1,2,3}, B= {2,3,4} and R is a relation from A to B.Then, the elements of AxB are.AxB = {(1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3.2), (3.3), (3,4)}Now, R is relation ‘is less than’ From A to B, so the ordered paires of R = {(x,y)x<y} are R= {(1,2); (1,3); (1,4); (2,3); (2,4); (3,4)}If R be a relation from set A to set B, then the set of all the first components of theordered pairs belonging to R is called the domain of R.i.e. Domain (R) = {a∈A : (a,b)∈R For some b∈B} and the set of all secondcomponents of the ordered pairs belonging to R is called the range of R.i.e. Range (R) = {b∈B : (a,b)∈R for some a∈A}.Therefore, domain of R is {1,2,3} and range of R is {2,3,4}.B: Sketch the graph of R in Z x Z. Would R1 also be a relation from A to B?Justify your answer.Answer :
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