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Sets this is the first note of the semester and covers the basics such as sets, natural numbers, integers, ect.

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Wilfrid Laurier University
Shane Bauman

Sets A set is a collection of objects called the elements or members of the set. Ex. A= {Alice, bob, Cameron} - order doesn’t matter B= {2,3,4,5,6} - no repetition Sets can be written using a property B= {integers X such that 2≤X≤6} = {integers X: 2≤X≤6} 2εB – 2 is in the set 10ε\B – 10 is not in the set A set that has no elements is called the empty set or the void set and is denoted φ Two sets are equal if they have exactly the same elements If C= {6, 3, 4, 5, 2} then C=B If D= {2, 3, 4, 5, 7} then D≠B If E= {2, 3, 4, 5} then E≠B However E is a subset of B, we write Eʗ_ B (a set is a subset of itself) φʗ_ B Since E≠B we can write EʗB and we can say that E is a proper subset of B Set operations Let A and B be two sets. The union of A and B, denoted AUB is the set formed by elements that are in A or in B (or both) AUB= {X: XεA or XεB} ex. X= {2,4,6,8} Y= {2,3,5,8} XUY= {2,3,4,5,6,8} The intersection of A and B, denoted AηB is the set formed by elements that are in both A an
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