discrete math

Which one of the following options is correct for the given data in the table?

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential. If one wants to pur...

Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for...

Consider the binary relation: $$S = \left\{ {\left( {x,y} \right)|y = x + 1\,\,and\,\,x,y \in \left\{ {0,1,2,...} \right\}} \right\}$$ The reflexive transitive closure of $$S$$ is

The solution to the recurrence equation $$T\left( {{2^k}} \right)$$ $$ = 3T\left( {{2^{k - 1}}} \right) + 1$$, $$T\left( 1 \right) = 1$$ is:

The transitive closure of the relation $$\left\{ {\left( {1,2} \right)\left( {2,3} \right)\left( {3,4} \right)\left( {5,4} \right)} \right\}$$ on the set $$A = \left\{ {1,2,3,4,5}...