7) Consider two sets, S1 of size n and S2 of size m. How many relations are ther

Question

7) Consider two sets, S1 of size n and S2 of size m. How many relations are there from S1 to S2? N*m 8) How many onto mappings are there from a set of size 5(S1) to a set 9(S2)? (set S2) minimum 9 ? every point in codomain is value for atleast one point is S1 could be more than one. 9) How many 1-1 mappings are there from a set of size 5 to a set of size 5? 5 on each time individual 25 ? different ways Every element of first set is paired with one unique element of set 2. 10) How many partial mappings are there from a set of size 9 to a set of size 5? Partial mapping ? one or none Kp to 45 11) a) Define the notion of and algorithm. alogrithm- a finite set of steps used to solve a problem b) How do algorithms differ from processes? discrete math pt 2

Explanation / Answer

7.) total number of elements = number of elements in set 1 * number of elements in set 2

= m * n

8.) 0

no onto mapping is possible when n<m as 5 <9

9.) 1st element in set 1 can map with 5 elements in set 2nd

correponding to each of which 2st element in set 1 can map with 4 elements in set 2nd

going in same way solution = 5*4*3*2*1 = 120 = 5!

10.) partial mapping depends upon partial function its value depends upon partial function that we choose

11.) In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

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