# midterm-1 - Fall 2009 CS131 Combinatorial Structures...

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Fall 2009 CS131 – Combinatorial Structures Midterm exam 1 Midterm exam 1 Only a single hand-written “crib” sheet can be used, no books or notes. Even if I ask for just a yes/no answer, you must always give a proof. You may get some points even if you write “I don’t know”, but if you write something that is wrong, you may get less. (It is not possible to pass just writing “I don’t know” everywhere. ...) Problem 1. (10pt) Prove the relation A Δ B = ( A B ) ( A B ). Solution. By deﬁnition, A Δ B = ( A \ B ) ( B \ A ). Therefore A Δ B is the set of points that are in A or B , but not in both. Thus a point is not in A Δ B if it is in either both in A and in B , or it is in neither of them. Being in both means being in A B . Being in neither means not being in A and not being in B , that is being in A and being in B , that is being in A B . This shows that not being in A Δ B means being in ( A B ) ( A B ).

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## This note was uploaded on 10/15/2011 for the course MATHS 100 taught by Professor Fredphelps during the Fall '11 term at Jordan University of Science & Tech.

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midterm-1 - Fall 2009 CS131 Combinatorial Structures...

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