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handout3 - ECS20 Handout 3 January 6 2011 1 A set is an...

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ECS20 Handout 3 January 6, 2011 1. A set is an unordered colleciton of objects Notation: A,B,C,... 2. The objects in a set are also called the elements , or members , of the set. A set is said to contain its elements. 3. Two sets A and B are equal if and only if they have the same elements. A = B ↔ ∀ x ( x A x B ). 4. The set A is said to be a subset of B iff every element of A is also an element of B . A B ↔ ∀ x ( x A x B ). Proper subset: A B if x ( x A x B ) ∧ ∃ x ( x B x negationslash∈ A ). 5. For every set S , the empty (null) set Ø S and S S . 6. Universal set U contains all objectives under considerations. 7. Venn diagram 8. If there are n distinct elements in the set S where n is a nonnegative integer, we say that S is a finite set. n = | S | is the cardinality of S . A set is said to be infinite if it is not finite. 9. Given a set S , the power set of S is the set of all subset of S , denoted P ( S ) e.g. Let S = { 0 , 1 , 2 , } , then P ( S ) = 10. The ordered n -tuple ( a 1 ,a 2 ,...,a n ) is the
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