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# comments - is the empty set± it has no elements The set...

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In Question 1 you had to remember in each part to give the cardinality of the set. In Question 1 part (a), the expression x j 21 means that 21 is divisible by x . That is, 21 is a multiple of x . That is, 21 = mx for some integer m . So, for example, ° 21 j 21 and 1 j 21 and 3 j 21 . In Question 1 part (b) there seemed to be confusion between x ± f 1 ; 2 ; 3 ; 4 g , which means that x is a subset of f 1 ; 2 ; 3 ; 4 g , and x 2 f 1 ; 2 ; 3 ; 4 g , which means that x is an element of f 1 ; 2 ; 3 ; 4 g . The subsets of f 1 ; 2 ; 3 ; 4 g are things like ; and f 1 ; 3 g , the elements of f 1 ; 2 ; 3 ; 4 g are things like 1 and 3 . In Question 1 part (e), the set 2 f 3 ; 4 ; 5 g is the power set of f 3 ; 4 ; 5 g , the set of all subsets of f 3 ; 4 ; 5 g . It would make sense to de°ne 2 f 3 ; 4 ; 5 g to be f 2 3 ; 2 4 ; 2 5 g , but the textbook does not do that. The set
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Unformatted text preview: ; is the empty set± it has no elements. The set f;g has exactly one element, the empty set. You must make that distinction. So ; ± f 1 ; 2 ; 3 g , because every element of ; is an element of f 1 ; 2 ; 3 g , but it²s not true that f;g ± f 1 ; 2 ; 3 g because ; 6 = 1 and ; 6 = 2 and ; 6 = 3 . You also have to make the distinction between (1 ; 3) , which is an ordered pair, and f 1 ; 3 g , which is a set. The set f 1 ; 3 g is an element of 2 f 1 ; 2 ; 3 g while the ordered pair (1 ; 3) is an element of f 1 ; 2 g ² f 3 ; 4 ; 5 g . 1...
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