CBMA2103MATHEMATICDISCRETEASSIGNMENTStudent id and name [Pick the date]
Question 1 Universal 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 2 The given diagram represents set V such that V={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 from a¿b with 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 since aRb∧bRc and then the total number of flights required to flyfrom a¿c is 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
End of preview
Want to access all the pages? Upload your documents or become a member.
Related Documents
Assignment on Discrete Mathematicslg...
|8
|653
|457
DISCRETE MATHS.lg...
|6
|654
|2
Discrete Mathematics Assignmentlg...
|6
|495
|371
Complex Waveforms & Transients in R-L-C Circuitslg...