 So let's look at the some of the properties of binary relations in the first one And we want to that I want to look at is this the reflexive property the flex of property and we say a binary relation is reflective if the following holds the binary relation on a set a is reflective if a comma a is an element of that Relation for all elements a that are all elements a that are elements of a of the set a So reflexive means if I take any element in that set and I look at the binary relations on that element So for all of them I Have that this a comma a is an element of that relation so before we saw all the relations If I had there was one that had five comma five and six comma six if for everyone is like that And certainly it wasn't true for all of those then what would be to say for the first one that we had Divide because one divides one two divides two three divides three four divides four and five divides five So that would have been an example of a reflexive Let's have a look at one more example if we say something for instance this that are is Is equal to the is equal to Equal to or greater than Greater than That is my is equal to or greater than and my set Let's say my set is the set of all the real numbers no matter what real number I take it is equal to or greater than itself. It's always going to be equal to itself. So every element in our Every element in our if this is my relation that I'm looking for is a reflexive Relation the next one. We want to never look at let me just put it here. It's just symmetric the symmetric property of binary of binary relations that just means the following that if I have Say that a comma b is an element of our then B comma a is Also an element of our and this is where this is where you have to be careful Just check what your textbook no lecture is doing which way around there are they are they are writing it But if this is so and that is so for the relation on a set a binary relation on a set Then we're talking about a sorry about a symmetric set and the last one we're going to do is a transitive transitive the transitive property of a binary relation and in a great example It's always given in textbooks if you consider all the lines in the in the plane So I have two-dimensional plane x and y axis and I draw all the lines and My if my relation is so my set a let's just write that set a is all lines Lines in the plane and my that is my that is my Let's let's say my relation then is is parallel to each other is parallel Is parallel that's my Now transitive means the following if I have the following if one line So line one is parallel to line two and Line two is parallel to line three Then what holds well line one is parallel to line three Line one is parallel to line two and two is parallel to three that means one will be parallel to three so if I have this and For all the for all the elements that I do have in that set of I have this property then that binary relation is Transitive so we have this reflexive property the symmetric property and the transitive properties the three properties that you should be aware of