Distinct relations in sets
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Having done only set theory (or more specifically, trying to grasp it) so far, can someone explain what's meant with distinct relations in sets?
For example, assuming I have the sets: A={a, b} and B={c, d, e} and I would want to find out the distinct relations from A to B, how would one solve this and what's the meaning behind it?
elementary-set-theory relations
asked Nov 16 at 21:09
K. Meyer
11
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show 2 more comments
up vote
0
down vote
favorite
Having done only set theory (or more specifically, trying to grasp it) so far, can someone explain what's meant with distinct relations in sets?
For example, assuming I have the sets: A={a, b} and B={c, d, e} and I would want to find out the distinct relations from A to B, how would one solve this and what's the meaning behind it?
elementary-set-theory relations
asked Nov 16 at 21:09
K. Meyer
11
1
Please provide more context.
– Berci
Nov 16 at 21:14
1
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27
|
show 2 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Having done only set theory (or more specifically, trying to grasp it) so far, can someone explain what's meant with distinct relations in sets?
For example, assuming I have the sets: A={a, b} and B={c, d, e} and I would want to find out the distinct relations from A to B, how would one solve this and what's the meaning behind it?
elementary-set-theory relations
asked Nov 16 at 21:09
K. Meyer
11
Having done only set theory (or more specifically, trying to grasp it) so far, can someone explain what's meant with distinct relations in sets?
For example, assuming I have the sets: A={a, b} and B={c, d, e} and I would want to find out the distinct relations from A to B, how would one solve this and what's the meaning behind it?
elementary-set-theory relations
elementary-set-theory relations
asked Nov 16 at 21:09
K. Meyer
11
asked Nov 16 at 21:09
K. Meyer
11
asked Nov 16 at 21:09
K. Meyer
11
asked Nov 16 at 21:09
K. Meyer
11
asked Nov 16 at 21:09
K. Meyer
11
11
1
Please provide more context.
– Berci
Nov 16 at 21:14
1
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27
|
show 2 more comments
1
Please provide more context.
– Berci
Nov 16 at 21:14
1
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27
1
1
Please provide more context.
– Berci
Nov 16 at 21:14
Please provide more context.
– Berci
Nov 16 at 21:14
1
1
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27
|
show 2 more comments
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1
Please provide more context.
– Berci
Nov 16 at 21:14
1
The term "distinct relation" has no standard meaning, unless the word "distinct" is just for emphasis and it merely means to list all the relations from $A$ to $B$.
– Eric Wofsey
Nov 16 at 21:19
So basically just A x B?
– K. Meyer
Nov 16 at 21:22
Remember that a relation from $A$ to $B$ is merely a subset of $Atimes B$. One example of a relation from $A$ to $B$ is the relation ${(a,c),(a,d),(a,e)}$. Another example is ${(a,c),(b,d)}$. Yet another would be $emptyset$. The list goes on. If you want to actually write them all out, you can follow a simple algorithm to do so, but noone generally bothers, it is easier to refer to the set of all relations from $A$ to $B$ simply as $mathcal{P}(Atimes B)$ where $mathcal{P}(~)$ refers to the powerset. The number of such relations would be $2^{|A|times |B|}$
– JMoravitz
Nov 16 at 21:22
People use relations all the time in their everyday life, we just have specific names for those relations. For example, let $A$ be the set of English letters ${a,b,c,d,dots,z}$ and let $B$ be the set of English words appearing in the Oxford Dictionary: $B={text{aardvark, abacus, abate},dots}$. Then one example of a relation is the "is the first letter of" relation, where $a$ is related to "aardvark" since the first letter of "aardvark" is $a$. A different relation would be "is a letter in" where not only is $a$ related to "aardvark" but so too is $d$ and $v$ etc...
– JMoravitz
Nov 16 at 21:27