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Unformatted text preview: MAT 125a, HW1 Solutions 5 (a) (i) First assume x B { i I X i } . Since x B { i I X i } we have that x B and j I such that x X j . Since x B and x X j we have x B X j i I ( B X i ). So x B { i I X i } implies x i I ( B X i ) hence B { i I X i } i I ( B X i ). (ii) Next assume x i I ( B X i ). Since x i I ( B X i ) j I such that x B X j . Since x B X j we have that x B and x X j hence x B and x i I X i which implies that x B { i I X i } . Therefore i I ( B X i ) B { i I X i } . Therefore by (i) and (ii) we have i I ( B X i ) = B { i I X i } . (b) (i) First assume x ( i I X i ) { . Since x ( i I X i ) { we have that x S and x 6 i I X i which implies that x S and x 6 X i i I . Since x S and i I s 6 X i we have that x X { i i I and hence x i I X { i . Therefore....
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 Spring '10
 anne
 Number Theory

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