Chapter 1.4, Problem 10E

a .

To determine

To find: if the set of ordered pairs $\left\{\left(a,1\right),\left(c,2\right),\left(c,3\right),\left(b,3\right)\right\}$ represents function from $A=\left\{a,b,c\right\}$ to $B=\left\{0,1,2,3\right\}$ .

Answer to Problem 10E

Not a function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(a,1\right),\left(c,2\right),\left(c,3\right),\left(b,3\right)\right\}$ is not a function because the element c belonging to the set $A=\left\{a,b,c\right\}$ is assigned to two elements ‘2’ and ‘3’ in the set $B=\left\{0,1,2,3\right\}$ .

b.

To determine

To find: if the set of ordered pairs $\left\{\left(a,1\right),\left(b,2\right),\left(c,3\right)\right\}$ represents function from $A=\left\{a,b,c\right\}$ to $B=\left\{0,1,2,3\right\}$ .

Answer to Problem 10E

Function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(a,1\right),\left(b,2\right),\left(c,3\right)\right\}$ represents a function because each element in set $A=\left\{a,b,c\right\}$ is assigned to exactly one element of set $B=\left\{0,1,2,3\right\}$ .

c .

To determine

To find: if the set of ordered pairs $\left\{\left(1,a\right),\left(0,a\right),\left(2,c\right),\left(3,b\right)\right\}$ represents function from $A=\left\{a,b,c\right\}$ to $B=\left\{0,1,2,3\right\}$ .

Answer to Problem 10E

Not a function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(1,a\right),\left(0,a\right),\left(2,c\right),\left(3,b\right)\right\}$ does not represent a function because the elements 0, 1, 2 and 3 do not belong to the domain $A=\left\{a,b,c\right\}$ .

d.

To determine

To find: if the set of ordered pairs $\left\{\left(c,0\right),\left(b,0\right),\left(a,3\right)\right\}$ represents function from $A=\left\{a,b,c\right\}$ to $B=\left\{0,1,2,3\right\}$ .

Answer to Problem 10E

Function

Explanation of Solution

Concept Used:

Function: A function is a relation which maps each element belonging to set A to exactly one element belonging to the set B.

The given set of ordered pairs $\left\{\left(c,0\right),\left(b,0\right),\left(a,3\right)\right\}$ represents a function because each element in the domain $A=\left\{a,b,c\right\}$ is assigned to exactly one element of set $B=\left\{0,1,2,3\right\}$ .