This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: B . (a) (1 point) Show that f ( ∪ i ∈ I A i ) = ∪ i ∈ I f ( A i ). (b) (1 point) Suppose f is a bijection. Show that f − 1 ( ∩ i ∈ J B j ) = ∩ j ∈ J f − 1 ( B j ). Problem 6: (1 points) ±or following functions, ²nd f ( A ) and f − 1 ( B ). (a) (0.5 point) f : R → R is de²ned by f ( x ) = sin x , A = {− 2 , − 1 , , 1 , 2 } , B = { , 1 , 2 } . (b) (0.5 point) f : R → Z is is the ³oor function de²ned by f ( x ) = ⌊ x ⌋ = n where n ≤ x < n + 1 for n ∈ N and A = (0 , 5), B = { , 1 , 2 } . Problem 7: (2 points) Let f : A → B and B ′ ⊆ B . (a) (1 point) Prove that f ( f − 1 ( B ′ ) ) ⊆ B ′ . (b) (1 point) Prove that if f is onto, then f ( f − 1 ( B ′ ) ) = B ′ . Problem 8: (1 point) Prove or ²nd a counterexample to the following conjecture. Assume f : X → Y and A, B ⊂ X If f ( A ) \ f ( B ) = ∅ , then f ( A \ B ) = ∅ . 2...
View
Full Document
 Fall '07
 SCHMIDT
 Elementary algebra, Multiplicative inverse

Click to edit the document details