Associativity

[Sonal7]

I am unsure who do part 1.3 using table 1.4. Could someone give an example and show how one of the ans is done.

 

[Sonal7]

* how one of the ans is derived. I apologise about the grammar. I know what associativity is a*(b*c) =(a*b)*c.
but the operation can only take 2 inputs so I am very confused.

 

[Sonal7]

I am sorry to waste everyones time but I got it now. I was having a doze when i realised that you just do a*b get the solution and then do the next one...so on. Solved!

 

[Dr.Peterson]

I am sorry to waste everyones time but I got it now. I was having a doze when i realised that you just do a*b get the solution and then do the next one...so on. Solved!

I'm not sure how you use a*b to fill in the row for d. Just to make sure you've really solved it, can you show us how you found one of the missing values?

 

[Sonal7]

I'm not sure how you use a*b to fill in the row for d. Just to make sure you've really solved it, can you show us how you found one of the missing values?

Hi Dr Peterson. I am sorry about the late reply. I chose random alphabets and used the binary operation b*(a*d) and (b*a)*d. I think using trial worked out which alphabet gives the same ans. The d was worked out without using associativity, a* any alphabet returns the same alphabet. d*any alphabet returns d. so I followed the pattern. For the others I solved using associativity. so for the 2nd missing alphabet, lets use the example b*a*d, if we compute (b*a) we get b. Now b*d something will give you something, but we can see that might be c. i am not that sure anymore!?

 

[Dr.Peterson]

Hi Dr Peterson. I am sorry about the late reply. I chose random alphabets and used the binary operation b*(a*d) and (b*a)*d. I think using trial worked out which alphabet gives the same ans. The d was worked out without using associativity, a* any alphabet returns the same alphabet. d*any alphabet returns d. so I followed the pattern. For the others I solved using associativity. so for the 2nd missing alphabet, lets use the example b*a*d, if we compute (b*a) we get b. Now b*d something will give you something, but we can see that might be c. i am not that sure anymore!?

Your "random alphabets" should be "random letters"; an alphabet is a set of letters. But I know this is a common usage, particularly among students in south Asia I've interacted with, so maybe it is considered correct for you.

Anyway, one thing I was concerned about was that you might be assuming things that are not stated, such as that a is an identity. Since you are told only that this is an associative binary operation, you can't make such an assumption. So you made two reasonable guesses, but that is all they are.

All I see to do is to try "random" combinations of three elements. Since you are not given d*anything, you have to use combinations that yield d.

Try using c*b*a, for instance. As (c*b)*a, that's d*a; what do you find that equals?

Then do the same for the rest of the row.

 

[Sonal7]

Your "random alphabets" should be "random letters"; an alphabet is a set of letters. But I know this is a common usage, particularly among students in south Asia I've interacted with, so maybe it is considered correct for you.

Anyway, one thing I was concerned about was that you might be assuming things that are not stated, such as that a is an identity. Since you are told only that this is an associative binary operation, you can't make such an assumption. So you made two reasonable guesses, but that is all they are.

All I see to do is to try "random" combinations of three elements. Since you are not given d*anything, you have to use combinations that yield d.

Try using c*b*a, for instance. As (c*b)*a, that's d*a; what do you find that equals?

Then do the same for the rest of the row.

No I just have poor vocabulary. I checked in Cambridge online dictionary and you are right. Asians cant make bad english into correct form of english. In fact, foreigners adhere to english grammar better than some english people as rely on formal teaching rather than learning from peers. I know American usage of some words differ. I know know why I didnt cotton on, as they do say the letters of the greek alphabet are .... Its just me not picking up the meaning behind he words!

Anyway I need to check this out.