 So then let's just finish this little section of we've got these two examples and we're just looking at the two at least two types of binary operations and one is commutative commutative and We've looked at that. So I said that that's not commutative Because of that. Let's look at this it is commutative We've already seen if we if we swap these first and second elements around of these order pairs that we do get to the same Just have a quick look at this. Just note something for later on We note that there's no repetition of my elements if I go down any of the rows and any of the columns and if I go down my main diagonal here And if I look across from that and if I look across from that B and B I get C and C D I Get the let me just see the ease and the ease and I get a and a and I get the B's And I get to see that so there's certainly some metric So there's simply something about this table as we've written out So that is the commutative type of binary operation and then of course we get associative associative type of Binary of binary operations now. Let's have a look. Let's let's have a look at this one. So I'm going to have a and B C and I'm going to have a and B and then C So what is this going to be? Well, I'm just giving it the first element of any of that So it's going to be a and B and that is going to equal a And if I do this well, that is going to be a C and that is a and they are exactly equal So definitely this would be associative is this one associative is this one associative. So let's do a And B as well with C and let's do a with B and C So a and B if I go to A and B, that's B So that is B with C and if I go with B with C, I get D And if I go B with C, B with C, that's D So that's A and D and if I go A to D, I also get D So definitely have a look at that let this binary operation on the set is associative just as this is this one is commutative that one is not commutative And now you can just play around with the normals you can look at what is addition What is the let's say What is the positive Positive rational numbers under addition Under the operation of addition just look at these see if you can figure out whether it commutes and whether it is associative