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Sets Functions Injectivity Surjectivity Composition

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Part (i) Let S be the set of all non-empty subsets of [1,2,4). Explain whether the following are functions with a suitable codomain. For those that are functions, explain whether they are one-to- one (injective) and what the codomain would need to be for them to be onto (surjective). [8 points] (a) c(a)=A for any set AS (b) s(A) is the sum of all elements in a set AS (c) p(A) is the product of all elements in a set AS (d) I(A) is the largest element in a set AS. Part (ii) Let e:AB and f:BC be functions for some arbitrary sets A,B, and C. Prove or disproise the following [ 4 points]: If fe is one-to-one (injective), then f is one-to-one (injective)..

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Part (i) Let S be the set of all non-empty subsets of [1,2,4). Explain whether the following are functions with a suitable codomain. For those that are functions, explain whether they are one-to- one (injective) and what the codomain would need to be for them to be onto (surjective). [8 points] (a) c(a)=A for any set AS (b) s(A) is the sum of all elements in a set AS (c) p(A) is the product of all elements in a set AS (d) I(A) is the largest element in a set AS. Part (ii) Let e:AB and f:BC be functions for some arbitrary sets A,B, and C. Prove or disproise the following [ 4 points]: If fe is one-to-one (injective), then f is one-to-one (injective).

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Sets Functions Injectivity Surjectivity Composition

  • 1. Part (i) Let S be the set of all non-empty subsets of [1,2,4). Explain whether the following are functions with a suitable codomain. For those that are functions, explain whether they are one-to- one (injective) and what the codomain would need to be for them to be onto (surjective). [8 points] (a) c(a)=A for any set AS (b) s(A) is the sum of all elements in a set AS (c) p(A) is the product of all elements in a set AS (d) I(A) is the largest element in a set AS. Part (ii) Let e:AB and f:BC be functions for some arbitrary sets A,B, and C. Prove or disproise the following [ 4 points]: If fe is one-to-one (injective), then f is one-to-one (injective).