# lecture14 - This lecture will not be conducted physically...

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MA1100 Lecture 14 Relations Representation of relation Domain and range of relation Reflexive, symmetric, transitive relation Chartrand: 8.1, 8.2 This lecture will not be conducted physically at LT27 on Oct 6. It will only be available on IVLE in webcast format from Oct 6 onward.

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Lecture 14 2 Online quiz ± This lecture comes with an online quiz, which will be available on IVLE from Oct 6, 12pm to Oct 8, 11,59pm. ± You may do the online quiz while viewing the webcast lecture, or after the lecture. ± View the webcast for this lecture for more detailed instruction.
Lecture 14 3 Divisibility Relation Example We call this a relation from A to B. Which elements of A divides an element of B? an association of an object with another object Let A = {0, 1, 2} and B = {0, 1, 2, 3, 4} 0 (in A) divides 0 (in B) 1 (in A) divides every element in B 2 (in A) divides 0, 2, 4 (in B)

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Lecture 14 4 Father-Son Relation Example Who in F is the father of someone in S? F = {Tom, Dick, Harry} and S = {Alan, Bob, Carl} Tom (in F) is the father of Alan and Bob (in S) Dick (in F) is the father of Carl (in S) Harry (in F) is not the father of anyone (in S) This gives a relation from F to S.
Lecture 14 5 Relation To define a relation , we need two sets A and B , and a “rule” that decides whether an element in A is associated (or related) to an element in B. Together, this is called a relation from A to B . Under the rule, (i) some element of A (resp. B) may be related to none of the elements of B (resp. A) (ii) some element of A (resp. B) may be related to more than one element of B (resp. A) If a œ A is related to b œ B, we write a ~ b for short. If a is not related to b, we write a ~ b for short.

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{} Lecture 14 6 Ordered Pair Representation Example ( Divisibility Relation) Let A = {0, 1, 2} and B = {0, 1, 2, 3, 4} 0 (in A) divides 0 (in B) 1 (in A) divides every element in B 2 (in A) divides 0, 2, 4 (in B) (0, 0) (1, 0), (1, 1), (1, 2), (1, 3), (1, 4) (2, 0), (2, 2), (2, 4) R = R is the ordered pair representation of the divisibility relation from A to B Œ A ä B
Lecture 14 7 {} Ordered Pair Representation Example (Father-Son Relation) F = {Tom, Dick, Harry} and S = {Alan, Bob, Carl} Tom (in F) is the father of Alan and Bob (in S) Dick (in F) is the father of Carl (in S) (Tom, Alan), (Tom, Bob) (Dick, Carl) R = R is the ordered pair representation of the father- son relation from F to S.

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lecture14 - This lecture will not be conducted physically...

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