05Set_10

05Set_10 - ENGG1007 Foundations of Computer Science Sets...

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1 ENGG1007 Foundations of Computer Science Sets Sets Prof. Francis Chin, Dr SM Yiu Sept 20/22, 2010 (Chapter 2.1, 2.2)
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2 ENGG1007 FCS Sets Sets Definition & Notation Definition & Notation A set is a collection of objects . Example: A = {apple, orange, mango, pear} ; apple ‘apple’ B = {policeman, fireman, manager, doctor, lawyer} C= {1 , 2 } D = {1, house, john, apple, salmon} E = {1, 2, C} = {1, 2, {1, 2}} F= {F , 1 }
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3 ENGG1007 FCS Elements of a Set Elements of a Set The objects are called elements elements or members members of the set. A set is said to contain contain its elements. Notations: x S : x is an element of the set S. ) 2 { 5, 7, π , “apple”, 2, 2.718 } ) {1} { {1}, {a, b}, a, 1 } ) Given F = {F, 1}, F F ? x x S : x is not an element of the set S. ) apple { 5, 7, π , “apple”, 2, 2.718 } ) b { {1}, {a, b}, a, 1 }
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4 ENGG1007 FCS The Empty Set & The Universal Set The Empty Set & The Universal Set • The set that has no elements is called the empty set empty set or the null set null set , and is denoted by { } { } or . ¾ Note that mathematically, there is only one empty set. •T h e universal set universal set is the set containing all elements under consideration. A question A question : Is this, { { } , the empty set? ¾ Answer: No, this is a set containing 1 element, the empty set. • A set with 1 element is called a singleton singleton . ) e.g. { x }, { 1 }
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5 ENGG1007 FCS Finite and Infinite Sets Finite and Infinite Sets S is a finite set finite set : S contains exactly n elements ( n 0) | S | is the cardinality
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05Set_10 - ENGG1007 Foundations of Computer Science Sets...

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