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These two terms would be the simplest terms in the set theory as they are on the first chapter in my textbook. But why can't i understand it?
In my textbook it says
A relation R in a set is a set of ordered pairs, so any subset of a set of ordered pairs will be a relation. This includes the empty set which is referred to as the empty relation.
What is this mean? empty set = empty relation? and if so then why empty relation is symmetric as well as transitive? My teacher said it is done by default but i still can not understand it.
In case of equivalence class i understand the concept and i thought it was easy. An equivalnce relation on Set partitions Set into subsets which are called equivalence classes. Good enough not difficult. But in the example where
A = {1, 2, 3, 4} and define a relation R by: xRy <-> x + y is even.
The relation is equivalence relation. R = {(1, 1), (1, 3), (3, 3), (3, 1), (2, 2), (4, 4), (4, 2)}
and they say equivalence classes : {1, 3} and {2, 4}
This i can not understand.. why only these two? doesn't {1 ,1} {2, 2} {3, 3} {4, 4} counted?
Set theory is too hard..I thought i understood everything and when i look back everything is new! well that must be because i couldn't have enough time for revision but this is too much.
Any definitions of empty relation and equivalence class that can be understood by person like me?
In my textbook it says
A relation R in a set is a set of ordered pairs, so any subset of a set of ordered pairs will be a relation. This includes the empty set which is referred to as the empty relation.
What is this mean? empty set = empty relation? and if so then why empty relation is symmetric as well as transitive? My teacher said it is done by default but i still can not understand it.
In case of equivalence class i understand the concept and i thought it was easy. An equivalnce relation on Set partitions Set into subsets which are called equivalence classes. Good enough not difficult. But in the example where
A = {1, 2, 3, 4} and define a relation R by: xRy <-> x + y is even.
The relation is equivalence relation. R = {(1, 1), (1, 3), (3, 3), (3, 1), (2, 2), (4, 4), (4, 2)}
and they say equivalence classes : {1, 3} and {2, 4}
This i can not understand.. why only these two? doesn't {1 ,1} {2, 2} {3, 3} {4, 4} counted?
Set theory is too hard..I thought i understood everything and when i look back everything is new! well that must be because i couldn't have enough time for revision but this is too much.
Any definitions of empty relation and equivalence class that can be understood by person like me?