Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?

(i) f is a relation from A to B

(ii) f is a function from A to B.

Asked by Abhisek | 11 months ago |  120

##### Solution :-

Given,

A = {1, 2, 3, 4} and B = {1, 5, 9, 11, 15, 16}

So,

A × B = {(1, 1), (1, 5), (1, 9), (1, 11), (1, 15), (1, 16), (2, 1),

(2, 5), (2, 9), (2, 11), (2, 15), (2, 16), (3, 1), (3, 5), (3, 9),

(3, 11), (3, 15), (3, 16), (4, 1), (4, 5), (4, 9), (4, 11), (4, 15), (4, 16)}

Also given that,

f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B.

It’s clearly seen that f is a subset of A × B.

Therefore, f is a relation from A to B.

(ii) As the same first element If we check carefully, we see that the first element 2 is providing us two different value of the image 9,11 .

So, it can be concluded that f is not a function from A to B.

Answered by Pragya Singh | 11 months ago

### Related Questions

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#### Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

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#### If A = {5} and B = {5, 6}, write down all possible subsets of A × B.

If A = {5} and B = {5, 6}, write down all possible subsets of A × B.
The content structure of the provided text passage is a mathematical problem involving sets and relations, with a solution provided for the given problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?

(i) f is a relation from A to B

(ii) f is a function from A to B.

Asked by Abhisek | 11 months ago |  120

##### Solution :-

Given,

A = {1, 2, 3, 4} and B = {1, 5, 9, 11, 15, 16}

So,

A × B = {(1, 1), (1, 5), (1, 9), (1, 11), (1, 15), (1, 16), (2, 1),

(2, 5), (2, 9), (2, 11), (2, 15), (2, 16), (3, 1), (3, 5), (3, 9),

(3, 11), (3, 15), (3, 16), (4, 1), (4, 5), (4, 9), (4, 11), (4, 15), (4, 16)}

Also given that,

f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

(i) A relation from a non-empty set A to a non-empty set B is a subset of the Cartesian product A × B.

It’s clearly seen that f is a subset of A × B.

Therefore, f is a relation from A to B.

(ii) As the same first element If we check carefully, we see that the first element 2 is providing us two different value of the image 9,11 .

So, it can be concluded that f is not a function from A to B.

Answered by Pragya Singh | 11 months ago

### Related Questions

#### Let R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N

Let R = {(a, b) : a, b, ϵ N and a < b}.Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.

#### Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

Let A = (1, 2, 3} and B = {4} How many relations can be defined from A to B.

#### Let R = {(x, x2) : x is a prime number less than 10}.

Let R = {(x, x2) : x is a prime number less than 10}.

(i) Write R in roster form.

(ii) Find dom (R) and range (R).

#### If A = {5} and B = {5, 6}, write down all possible subsets of A × B.

If A = {5} and B = {5, 6}, write down all possible subsets of A × B.
user
The content structure of the provided text passage is a mathematical problem involving sets and relations, with a solution provided for the given problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER