COS1501 Assignment 3 (COMPLETE ANSWERS) 2024 (653581) - DUE 22 July 2024

COS1501 Assignment 3 (COMPLETE ANSWERS) 2024 (653581) - DUE 22

July 2024

Question 1 Complete Marked out of 2.00 Question 2 Complete Marked out of

2.00 QUIZ Suppose U = {1, 2, 3, 4, 5, a, b, c} is a universal set with the subset

A = {a, b, c, 1, 2, 3, 4}. Which one of the following relations on A is NOT

functional? a. {(1, 3), (b, 3), (1, 4), (b, 2), (c, 2)} b. {(a, c), (b, c), (c, b), (1, 3),

(2, 3), (3, a)} c. {(a, a), (c, c), (2, 2), (3, 3), (4, 4)} d. {(a, c), (b, c), (1, 3), (3, 3)}

Suppose U = {1, 2, 3, 4, 5, a, b, c} is a universal set with the subset A = {a, b,

c, 1, 2, 3, 4}. Which one of the following alternatives represents a surjective

function from U to A? a. {(1, 4), (2, b), (3, 3), (4, 3), (5, a), (a, c), (b, 1), (c, b)}

b. {(a, 1), (b, 2), (c, a), (1, 4), (2, b), (3, 3), (4, c)} c. {(1, a), (2, c), (3, b), (4, 1),

(a, c), (b, 2), (c, 3)} d. {(1, a), (2, b), (3, 4), (4, 3), (5, c), (a, a), (b, 1), (c, 2)}

Question 3 Complete Marked out of 2.00 Question 4 Complete Marked out of

2.00 Question 5 Complete Marked out of 2.00 Let G and L be relations on A =

{1, 2, 3, 4} with G = {(1, 2), (2, 3), (4, 3)} and L = {(2, 2), (1, 3), (3, 4)}. Which

one of the following alternatives represents the relation L ￮ G = G; L? a. {(2,

3), (3, 3)} b. {(1, 2), (2, 4), (4, 4)} c. {(1, 2), (2, 1), (3, 3), (4, 4)} d. {(2, 4), (4, 4)}

Let g be a function from Z (the set of positive integers) to Q (the set of rational

numbers) defi ned by (x, y) ∈ g iff y = (g ⊆ Z x Q) and let f be a function on Z

defi ned by (x, y) ∈ f iff y = 5x + 2x – 3 (f ⊆ Z x Z ). Consider the function f on Z

. For which values of x is it the case that 5x + 2x – 3 > 0? Hint: Solve 5x + 2x –


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, 3 > 0 and keep in mind that x ∈ Z . a. x < 5, x ∈ Z b. < x <1, x ∈ Z c. x ≥ 1, x ∈

Z d. x < 1, x ∈ Z + 4x − 3/7 + + 2 + + + 2 2 + + 3/5 + + + Let g be a function

from Z (the set of positive integers) to Q (the set of rational numbers) defi ned

by (x, y) ∈ g iff y = (g ⊆ Z x Q) and let f be a function on Z defi ned by (x, y) ∈ f

iff y = 5x + 2x – 3 (f ⊆ Z x Z ). Which one of the following is an ordered pair

belonging to f? a. (–1, 0) b. (2, 21) c. (1, 5) d. (3, 44) + 4x − 3/7 + + 2 + +

Question 6 Complete Marked out of 2.00 Question 7 Complete Marked out of

2.00 Question 8 Complete Marked out of 2.00 Let g be a function from Z (the

set of positive integers) to Q (the set of rational numbers) defi ned by (x, y) ∈ g

iff y = (g ⊆ Z x Q) and let f be a function on Z defi ned by (x, y) ∈ f iff y = 5x +

2x – 3 (f ⊆ Z x Z ). Which one of the following alternatives represents the

image of x under g ￮ f (ie g ￮ f(x)))? a. 20x + 8x – 12 b. 80x + 4 x – c. 20x + 8x

+ 3 d. 80x + 4 x – 3 + 4x − 3/7 + + 2 + + 2 3/7 2 4/7 180/49 2 3/7 2 4/7 Let g

be a function from Z (the set of positive integers) to Q (the set of rational

numbers) defi ned by (x, y) ∈ g iff y = (g ⊆ Z x Q), and let f be a function on Z

defi ned by (x, y) ∈ f iff y = 5x + 2x – 3 (f ⊆ Z x Z ). Which one of the following

statements regarding the function g is TRUE? (Remember, g ⊆ Z x Q.) a. g

can be presented as a straight line graph. b. g is injective. c. g is surjective. d.

g is bijective. + 4x − 3/7 + + 2 + + + Which one of the following alternatives

gives the format for the list notation of a. (((a, a), a), ((a, b), d), ((a, c), c), ((a,

d), b), ((b, a), b), ((b, b), a), ((b, c), d), ((b, d), a), ((c, a), c), ((c, b), b), ((c, c),

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