In analogy with defintion 1.25a, we define the following:
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If A and B are subsets of <B>R</B>, then 
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A+B := {x+y : x element of A and y element of B}
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Likewise 
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A.B := { xy : x element of A and y element of B }
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(1) Show that A + (-A) is always a symmetric set. `Always' means: 
   For *every* subset A of <B>R</B>, A + (-A) is symmetric.
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(2) Decide whether A.(-A) is always symmetric or not. 
   Give a proof or counterexample, as appropriate.