Lecture_13 - MA1100 Lecture 13 Relations Representation of...

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1 MA1100 Lecture 13 Relations Representation of relation Domain and range of relation Reflexive, symmetric, transitive relation
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MA1100 Lecture 13 2 Announcement Mid-term test Will be returned to you either next week or the week after during tutorial class. Homework 3 To be handed in on Oct 7 (next Tuesday) Submit only solutions from problem set 5 (Mathematical Induction).
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Lesson Plan (week 7 to 13) No Tut 13. Relations Test Week 7 HW4 PS6/7 Tut 7 Functions 19. Number Th. 18. Functions Week 10 Tut 6 Relations 17. Functions 16. Functions Week 9 HW3 PS5 Tut 5 Math. Ind. 15. Relations 14. Relations Week 8 Tut 10 Misc Tut 9 Number Th. Tut 8 Functions Tutorial HW5 PS8/9 23. Revision lecture 22. Revision lecture Week 12 Week 13 21. Number Th. 20. Number Th. Week 11 HW Fri Lecture Tue Lecture
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MA1100 Lecture 13 4 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) gives all possible associations from elements in A to elements in B
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MA1100 Lecture 13 5 Father-Son Relation Example Who in A is the father of someone in B? A = {Tom, Dick, Harry} and B = {Alan, Bob, Carl} Tom (in A) is the father of Alan and Bob (in B) Dick (in A) is the father of Carl (in B) Harry (in A) is not the father of anyone (in B) This gives a relation from A to B.
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MA1100 Lecture 13 6 Relation A relation from a set A to a set B associates an element in A to an element in B in a specific way. (i) Certain element of A may not be associated to any element of B; (ii) Certain element of A may be associated to more than one element of B; (iii) There may not be any element of A that is associated to certain element of B; (iv) When A = B, we say the relation is on the set A. e.g. divisibility can be a relation on Z
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MA1100 Lecture 13 7 Relation (Notation) We write a ~ b to denote the association of a œ A with b œ B under this relation. Let ~ denote a relation from a set A to a set B Father-son relation Tom ~ Alan Tom ~ Bob Dick ~ Carl Divisibility relation 0 | 0 (use | instead of ~) 2 | 0, 2 | 2, 2 | 4 Harry ~ Alan 0 | 1
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MA1100 Lecture 13 8 Relation (Notation) When we are discussing more than one relation from a set A to a set B, we may use ~ 1 , ~ 2 , etc to denote the relations.
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