Pls help with question 6 and 7. Help with just question 7 if u intend to • 3 help with just one question. | also asked 6 here cause it seems fairly short. a • • 1 • 2 C • d • • 4 Figure 1: An example of a bubble diagram for a function. Example 1. Figure 1 depicts a bubble diagram for a function from domain X = codomain Y = {1,2, 3, 4}. In this case, the range is equal to {1,2, 4}. {a, b, c, d} to Question 6. What properties does a bubble diagram have to have in order to represent a function? Question 7. There are eight different functions f : {a,b, c} → {0,1}. List them all by drawing bubble diagrams.

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Chapter2: Second-order Linear Odes
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My question is just question 7 and if possible 6 (cause it is short). Information from question 4 is required to answer qts 6&7 so I have attached that there. Pls do question 7 if u only intend to do one question out of questions  6 and 7 ( aka ignore qt6), I only added qt 6 here because it seems short. Thank you so much!  

Pls help with question 6
and 7. Help with just
question 7 if u intend to
•3 help with just one question.
I also asked 6 here cause it
seems fairly short.
a •
• 1
d •
• 4
X
Figure 1: An example of a bubble diagram for a function.
{а, b, с, а} to
Example 1. Figure 1 depicts a bubble diagram for a function from domain X
codomain Y
{1,2, 3, 4}. In this case, the range is equal to {1,2,4}.
Question 6. What properties does a bubble diagram have to have in order to represent a function?
Question 7. There are eight different functions f : {a,b, c} → {0, 1}. List them all by drawing
bubble diagrams.
Transcribed Image Text:Pls help with question 6 and 7. Help with just question 7 if u intend to •3 help with just one question. I also asked 6 here cause it seems fairly short. a • • 1 d • • 4 X Figure 1: An example of a bubble diagram for a function. {а, b, с, а} to Example 1. Figure 1 depicts a bubble diagram for a function from domain X codomain Y {1,2, 3, 4}. In this case, the range is equal to {1,2,4}. Question 6. What properties does a bubble diagram have to have in order to represent a function? Question 7. There are eight different functions f : {a,b, c} → {0, 1}. List them all by drawing bubble diagrams.
Question 4. Let X = {o,0,A, O} and Y = {a, b, c, d, e}. Determine whether each of the following
represent functions. Explain. If the relation is a function, determine the domain, codomain, and
range.
(a) ƒ : X → Y defined via f = {(0, a), (O, b), (A, c), (©, d)}. Needed info to answer qt
(b) g : X → Y defined via g =
{(o, a), (O, 6), (A, c), (O, c)}.
6 and 7 from another
image, which is my
(d) k : X → Y defined via k = {(0, a), (0, 6), (A, c), (0, d), (0, e)}. question. not this.
(c) h: X → Y defined via h = {(, a), (D, b), (A, c), (0, d)}.
(e) l: X → Y defined via l = {(0, e), (O, e), (A, e), (O, e)}.
(f) т: X — Y defined via т —
{(o, a), (A, b), (O, c)}.
(g) happy : Y → X defined via happy(y)
= © for all y E Y.
(h) id : X → X defined via id(x) = x for all x € X.
One useful representation of functions on finite sets is via bubble diagrams (like in Figure
12.3 of the textbook). To draw a bubble diagram for a function f : X → Y, draw one circle (i.e,
a “bubble") for each of X and Y and for each element of each set, put a dot in the corresponding
set. Typically, we draw X on the left and Y on the right. Next, draw an arrow from x e X to
УEY if f(*) — у (i.е., (х, у) € f).
Transcribed Image Text:Question 4. Let X = {o,0,A, O} and Y = {a, b, c, d, e}. Determine whether each of the following represent functions. Explain. If the relation is a function, determine the domain, codomain, and range. (a) ƒ : X → Y defined via f = {(0, a), (O, b), (A, c), (©, d)}. Needed info to answer qt (b) g : X → Y defined via g = {(o, a), (O, 6), (A, c), (O, c)}. 6 and 7 from another image, which is my (d) k : X → Y defined via k = {(0, a), (0, 6), (A, c), (0, d), (0, e)}. question. not this. (c) h: X → Y defined via h = {(, a), (D, b), (A, c), (0, d)}. (e) l: X → Y defined via l = {(0, e), (O, e), (A, e), (O, e)}. (f) т: X — Y defined via т — {(o, a), (A, b), (O, c)}. (g) happy : Y → X defined via happy(y) = © for all y E Y. (h) id : X → X defined via id(x) = x for all x € X. One useful representation of functions on finite sets is via bubble diagrams (like in Figure 12.3 of the textbook). To draw a bubble diagram for a function f : X → Y, draw one circle (i.e, a “bubble") for each of X and Y and for each element of each set, put a dot in the corresponding set. Typically, we draw X on the left and Y on the right. Next, draw an arrow from x e X to УEY if f(*) — у (i.е., (х, у) € f).
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