4/20/2017 Discrete Math 5.20PM 4.00 Test IV Show ALL your work Do NOT use a calc

Question

4/20/2017 Discrete Math 5.20PM 4.00 Test IV Show ALL your work Do NOT use a calculator In what follows, R is the set of real numbers and Z is the set of integers. L (a) Let fr (a,b, c, dh (a,b, c, d) be the function defined by f (a) b f(b) b (e e, f(d) a. (l) Is the function f one-to-one (ii) Is it onto? (b) Let f {a, b,c, d) ta,b, c, dh be the function defined by f(a) (b) f(c) c, f Is the function f one-to-one? (ii) Is it onto? II. Determine whether each of the following functions f z z is one-to-one. Show how you arrived at (c) f(ra) (b) f(n) (a) f(n) n 2 III. For i 1,2,3 let Fe fi, i 1,i+ 2,...1. Find each of the following. (c) (b) Fan Fen F (a) Fru FaUFa (d) F. IV. Determine whether each of the following functions f z x z Z is onto. Show how you arrived at (e) f(m,n) (b) f(m, n) (a) f(min) 3m v. Let A (a, 2), B (c, d, 2). C (z,v) and D m, n Find each of the following (e) A x C x D (b) B A (a) A B VI. Show that the sum of two odd integers is an even integer. VIL Determine whether each of the following statements is true or false. Give reason(s) for your answer. (c) ((5), 1) 1,5, ((5)) (b) (k,2) e (fk) 2. (2,1)) (a) 2) c fd, 2, 2, 3) VIII. List the elements of each of the following sets. s). (a) (n I n is a real number such that 5 3 48). (b) (m m is an integer such that 2rn 5 (d) l z is the square of an integer and z

Explanation / Answer

1)

a] f(a) = b ,f(b)=b ,f(c)=c ,f(d) = a

functions is not one -one as for a and b funtion value is same

function is not onto as range of function is not equal to codomain {a ,b,c,d}

b) f(a) =b , f(b) =a , f(c) =c and f(d) =d

function is one -one as for not 2 values of x ; f(x) gives sme result

function is onto as range = co-domain {a,b,c,d}

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