Binary Relations Between Sets A and B: Quick Question

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In summary: So for each ordered pair, we have 2 choices. Therefore, the total number of binary relations from A to B is 2^(|AxB|) = 2^(3x5) = 32768.In summary, there are 32768 binary relations from A to B, where A = {a,b,c} and B = {0,1,2,3,4}. This can be calculated by finding the total number of ordered pairs in AxB and multiplying it by 2, as each ordered pair can either be in the relation or not. Therefore, the total number of binary relations is 2^(3x5) = 32768.
  • #1
ktheo
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Homework Statement



True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.
 
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  • #2
ktheo said:

Homework Statement



True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

A "binary relation from A to B" is formally a subset of [itex]A \times B[/itex], so the number of such relations is the number of subsets of [itex]A \times B[/itex].
 
  • #3
ktheo said:

Homework Statement



True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

Try and work it out. How many total ordered pairs are there in AxB? Now each ordered pair can either be in the relation or not.
 

Related to Binary Relations Between Sets A and B: Quick Question

What is a "quick relations question"?

A "quick relations question" is a question that is typically asked in a social or personal context, and involves understanding or clarifying the relationship between two or more individuals.

Why is it important to ask quick relations questions?

Asking quick relations questions can help to improve communication and understanding in relationships. It allows individuals to express their thoughts and feelings, and can help to resolve conflicts or misunderstandings.

What are some examples of quick relations questions?

Some examples of quick relations questions include: "What do you think about our relationship?", "Can you explain why you feel that way?", "How do you think we can improve our communication?", or "What boundaries do you feel are important in our relationship?"

How can I approach asking a quick relations question without offending someone?

When asking a quick relations question, it is important to approach the conversation with empathy, honesty, and a desire to understand. Use "I" statements to express your feelings and avoid placing blame. Also, be open to hearing the other person's perspective and actively listen to their response.

How can asking quick relations questions benefit a scientific study?

In scientific studies, relationships between variables are often examined. Asking quick relations questions can help to clarify and understand the connection between these variables, leading to a deeper understanding of the phenomenon being studied.

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