Discrete Mathematics Answers

  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)

ii.   A = 1,2,3,4,5 B=1,2,3,4,5

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

Let X = {a, b, c} defined by f : X ®X such that f = {(a, b), (b, a), (c,c)}.  Find the values of

f^–1, f² and f⁴. 

a={x/x is the letters of the word mississippi}

StatethevalueofxafterthestatementifP(x)thenx:=1

b)x=1.

a)x=0.

isexecuted,whereP(x)isthestatement“x>1,”ifthe

valueofxwhenthisstatementisreachedis

c)x=2.

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.

i. A= v,w,x,y,z, B=1,2,3,4,5

R= (v,z),(w,1), (x,3),(y,5)

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

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

Let X = {a, b, c} defined by f : X (X such that f = {(a, b), (b, a), (c,c)}.  Find the values of f^1, f^2 and f^4. 

Draw the Hasse diagram of lattices, (L1,<) and (L2,<) where L1 = {1, 2, 3, 4, 6, 12} and L2 = {2, 3, 6, 12, 24} and a < b if and only if a divides b.

Let P be the power set of {a, b, c}. Draw the diagram of the partial order induced on P by the lattice (P,(,().

Show that p ⋁ (q ⋀ r) and (p ⋁ r) ∧ (p ⋁ r) are logically equivalent. This

is the distributive law of disjunction over conjunction.