MHB Concatenating Lists: Associative but Not Commutative/Idempotent

[Kenan1]

Hallo guys,
I'm looking for your help :). Here is a question from an Assigment, that i should tomorrow gave.

Explain that the concatenation of lists is associative but not commutative and not idempotent. (In this respect, there is one thing in common, however, two differences from the union.) Use as a symbol for the concatenation
K..L for lists K and L.
Thanks in Advance!

 

[HallsofIvy]

Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?

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Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?

- - - Updated - - -

Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?