### CBMA2103 Mathematic Discrete Assignment

Added on - 21 Apr 2020

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CBMA2103MATHEMATICDISCRETEASSIGNMENTStudent id and name[Pick the date]

Question 1Universal set and the subsets are given below:U={1,2,3,4,5,6}={x∈Z:1≤x≤6}A={2,34}={x∈Z:2≤x≤4}B={3,4,5}={x∈Z:3≤x≤5}(a)The respective sets are shown below:(i)A∪B={2,3,4,5}={x∈Z:2≤x≤5}(ii)A∩B={3,4}={x∈Z:3≤x≤4}(iii)A−B={2}(iv)B−A={5}(b)The respective Venn diagram to represent U, A and B is highlighted below:1

Question 2The given diagram represents set V such thatV={u,v,w,x,y,z}of the six cities and the directflights between them.(a)Relation R on V by aRb ( including zero flights and fly from a to b with the help of evennumber of flights)(i)“R is an equivalence relation on V”It is essential to note that R is an equivalence relation on V only when it would be reflexive,symmetric and transitive as highlighted below:Reflexive:(aRaforalla∈V)Symmetric:(aRarepresentsbRa)Transitive:(aRb∧bRcrepresentsaRc)It can be seen that the relation is reflexive. It is because one can fly from one city to same citywith the help of zero flight. Kindly note that zero is considered as even. Additionally, it issymmetric also because one can fly froma¿bwith the help of even number of flights. Similarly,if one wants to fly back from b to a then also they need even number of flights. This relation isalso considered as transitive sinceaRb∧bRcand then the total number of flights required to flyfroma¿cis mainly the sum of number of flights froma¿b∧also¿b¿c.Hence, the conclusioncan be made that R is an equivalence relation on V.(ii)“Partition the set into equivalence classes”For this, let one element in such a way that for the given cities which can be reached fromparticular city with the help of even number flights, there would be two equivalence classes.Hence, the partition the set into equivalence classes is true.2

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