Question

Which of the following relations is NOT a function?
a. The rule which assigns a capital city to each province.
b. The rule which assigns a President to each country.
c. The rule which assigns religion to each person.
d. The rule which assigns tourist spot to each province.​

Answer 1

(c) The rule which assigns religion to each person.

Step-by-step explanation:

Given

The rule which assigns a Capital city to each Province, President to each

Country,Religion to each Person and Tourist spot to each Province

To find

which relations is not a function,

A function is defined as a set of finite lists of objects, one for each combination of possible arguments.

Every function is a relations. However, not every relation is a function.In a function, there cannot be two lists that disagree on only the last element.

Here,

The rule which assigns religion to each person is not a function. Because, this relations is NOT a function.

Answer 2

Relation ,a province can have multiple tourist spot is one to many relation hence not a function.

Given:

• Statements about relations
• a. The rule which assigns a capital city to each province.
• b. The rule which assigns a President to each country.
• c. The rule which assigns religion to each person.
• d. The rule which assigns tourist spot to each province.​

To Find:

• Which relation is not a function

Solution:

If no two elements in the domain of f correspond to the same element in the range of f  then function is called one to one function

or relation is called one to one relation.

if more than one elements in the domain of f correspond to the same element in the range of f  then function is called Many to one function

Relation is called Many to  one  relation.

if  same elements in the domain of f correspond to the more than one elements in the range of f  then Relation is called one to many relation.

But Such relation is not a function

A function cannot be one-to-many because  any element in domain can have more than one out put

Every function is a relation but every relation is not a function.

a. The rule which assigns a capital city to each province.

Each province has one capital

so this is one to one relation hence a function

b. The rule which assigns a President to each country.

Each country  has only one president

so this is one to one relation hence a function

c. The rule which assigns religion to each person.

Each person  has only one religion

so this is one to one relation hence a function

d. The rule which assigns tourist spot to each province

A province can have multiple tourist spot

hence this is one to many relation hence not a function

Relation ,a province can have multiple tourist spot is one to many relation hence not a function.

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