Discrete Mathematics Answers

If a function is defined as f(x,n) mod n. Determine the

i.     Domain of f

ii.   Range of f

iii.   G(g(g(g(7)))) if g (n) = f(209, n).

Determine whether the following relations are injective and/or subjective function. Find universe of the  functions if they exist.

A = 1,2,3,4,5 B=1,2,3,4,5

           R = (1,2),(2,3),(3,4),(4,5),(5,1)

Determine whether the following relations are injective and/or subjective function. Find universe of the  functions if they exist.

i.     A= v,w,x,y,z, B=1,2,3,4,5

       R= (v,z),(w,1), (x,3),(y,5)

find the transitive closure of (1 3) (5 5) (1 6) (3 3) (5 6)

For divisibility relation on the set {1,3,6,9,12,5,25,125}, draw Hasse diagram. Then find minimal, maximal, greatest and least elements. Then give the topological sort using the divisibility relation

[P ۷ (P ۸ Q)] → R

If the truth value of (negation p ➡️ q) ➡️ ( p v negation r) is false, then what is the truth value negation p ↔️ r ?