Question

1. for each table below:

i) describe the relation in words.
ii) represent the relation:

• as a set of ordered pairs
• as an arrow diagram

a)
coin | value ($)
penny | 0.01
nickel | 0.05
dime | 0.10
quarter | 0.25
loonie | 1.00
toonie | 2.00
b)
sport | equipment
badminton | shuttlecock
badminton | racquet
hockey | puck
hockey | stick
tennis | ball
tennis | racquet
soccer | ball

1. consider the relation represented by this graph.

number of letters in a word
chart omitted

Explanation:

Part (a)

i) Describe the relation in words.

The relation shows the correspondence between different types of coins (penny, nickel, dime, quarter, loonie, toonie) and their respective monetary values in US dollars. Each coin is associated with a unique value.

ii) Represent the relation:

• As a set of ordered pairs: We take each coin as the first element and its corresponding value as the second element of the ordered pair. So the set is $\{( \text{penny}, 0.01), ( \text{nickel}, 0.05), ( \text{dime}, 0.10), ( \text{quarter}, 0.25), ( \text{loonie}, 1.00), ( \text{toonie}, 2.00) \}$.
• As an arrow diagram:
• We have two sets: the set of coins $\{ \text{penny}, \text{nickel}, \text{dime}, \text{quarter}, \text{loonie}, \text{toonie} \}$ and the set of values $\{ 0.01, 0.05, 0.10, 0.25, 1.00, 2.00 \}$.
• Draw an arrow from each coin to its corresponding value. For example, an arrow from "penny" to $0.01$, from "nickel" to $0.05$, and so on for all the coins.

Part (b)

i) Describe the relation in words.

The relation shows the correspondence between different sports (badminton, hockey, tennis, soccer) and the equipment used in those sports. Some sports (like badminton, hockey, tennis) are associated with more than one piece of equipment.

ii) Represent the relation:

• As a set of ordered pairs: We take each sport as the first element and the corresponding equipment as the second element. So the set is $\{( \text{badminton}, \text{shuttlecock}), ( \text{badminton}, \text{racquet}), ( \text{hockey}, \text{puck}), ( \text{hockey}, \text{stick}), ( \text{tennis}, \text{ball}), ( \text{tennis}, \text{racquet}), ( \text{soccer}, \text{ball}) \}$.
• As an arrow diagram:
• We have two sets: the set of sports $\{ \text{badminton}, \text{hockey}, \text{tennis}, \text{soccer} \}$ and the set of equipment $\{ \text{shuttlecock}, \text{racquet}, \text{puck}, \text{stick}, \text{ball} \}$.
• Draw an arrow from each sport to the equipment it uses. For example, two arrows from "badminton" (one to "shuttlecock" and one to "racquet"), two arrows from "hockey" (one to "puck" and one to "stick"), two arrows from "tennis" (one to "ball" and one to "racquet"), and one arrow from "soccer" to "ball".

Answer:

Part (a)

i) Describe the relation in words.

The relation shows the correspondence between different types of coins (penny, nickel, dime, quarter, loonie, toonie) and their respective monetary values in US dollars. Each coin is associated with a unique value.

ii) Represent the relation:

• As a set of ordered pairs: We take each coin as the first element and its corresponding value as the second element of the ordered pair. So the set is $\{( \text{penny}, 0.01), ( \text{nickel}, 0.05), ( \text{dime}, 0.10), ( \text{quarter}, 0.25), ( \text{loonie}, 1.00), ( \text{toonie}, 2.00) \}$.
• As an arrow diagram:
• We have two sets: the set of coins $\{ \text{penny}, \text{nickel}, \text{dime}, \text{quarter}, \text{loonie}, \text{toonie} \}$ and the set of values $\{ 0.01, 0.05, 0.10, 0.25, 1.00, 2.00 \}$.
• Draw an arrow from each coin to its corresponding value. For example, an arrow from "penny" to $0.01$, from "nickel" to $0.05$, and so on for all the coins.

Part (b)

i) Describe the relation in words.

The relation shows the correspondence between different sports (badminton, hockey, tennis, soccer) and the equipment used in those sports. Some sports (like badminton, hockey, tennis) are associated with more than one piece of equipment.

ii) Represent the relation:

• As a set of ordered pairs: We take each sport as the first element and the corresponding equipment as the second element. So the set is $\{( \text{badminton}, \text{shuttlecock}), ( \text{badminton}, \text{racquet}), ( \text{hockey}, \text{puck}), ( \text{hockey}, \text{stick}), ( \text{tennis}, \text{ball}), ( \text{tennis}, \text{racquet}), ( \text{soccer}, \text{ball}) \}$.
• As an arrow diagram:
• We have two sets: the set of sports $\{ \text{badminton}, \text{hockey}, \text{tennis}, \text{soccer} \}$ and the set of equipment $\{ \text{shuttlecock}, \text{racquet}, \text{puck}, \text{stick}, \text{ball} \}$.
• Draw an arrow from each sport to the equipment it uses. For example, two arrows from "badminton" (one to "shuttlecock" and one to "racquet"), two arrows from "hockey" (one to "puck" and one to "stick"), two arrows from "tennis" (one to "ball" and one to "racquet"), and one arrow from "soccer" to "ball".