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Discrete Mathematics Assignment

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Added on  2020-03-16

Discrete Mathematics Assignment

   Added on 2020-03-16

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Running head: DISCREET MATHEMATICS 1
Discrete Mathematics Assignment_1
DISCREET MATHEMATICS 21.No, if you take relation R on a set 1. 2, 3WhereR={(1,1),(1,2),(2,1),(1,3),(3,1),(2,2),(2,3)}The function is symmetric since for all x,yεRthereis(y,x)εRAlso, it is transitive as for all x,y,zεA,(x,y)εR,(y,z)εRthereis(x,z)εRDespite being transitive and symmetric the relation is not reflexive as forxεA,(x,x)εRismissingi.e. for x=3,(3,3)≠R2.A function f(x)isone to one iff an input yields a unique outputOn the other hand, a function is onto iff every element of the image has a preimageThe function f: Z6→Z6will be one to one and onto which is the same case for f: Z5→Z5A multiplicative inverse exists for the elements which are onto and one to one3.afbced
Discrete Mathematics Assignment_2
DISCREET MATHEMATICS 3In the question the vertices a, c, e and f all have vertices with odd degree of 3. Since a Euclerian path graph cannot have more than 2 vertices of odd degree G have no Euclerian path.Adding one edge to the graph flips the parities of the vertices it connects that is odd toeven and even to odd. We will add edge between two vertices of odd degree Adding ac gives fcdfaceabeThen adding efgivesafeabecdfc which now have a Euclerian path4.The vertices a, b, c, d, e, f is odd and of degree 3 and 1and g is an even vertex of 2Since a graph with a vertex of degree one cannot have a Hamilton circuit then G have no Hamiltonian cycle5.A minimum spanning tree has the minimum weight than any other spanning tree of a graphhthe total weight is 5+11+4=205a4f11cEdgeabacadaeafagahweight1843793284655
Discrete Mathematics Assignment_3

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