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Let f : X → Y, A¡ C X for all i e I and B; C Y for all j e J where I and J are some nonempty index sets. Prove the following statements. (a) f (Uier Ai) = Uier f(A;); (b) ƒ (Niei Ai) C Nier S(A;); (c) f- (Njej B;) = Njess(B;). Why wouldn't a set equality hold for part (b)? Explain.

Let f : X → Y, A¡ C X for all i e I and B; C Y for all j e J where I and J are some nonempty index sets. Prove the following statements. (a) f (Uier Ai) = Uier f(A;); (b) ƒ (Niei Ai) C Nier S(A;); (c) f- (Njej B;) = Njess(B;). Why wouldn't a set equality hold for part (b)? Explain.

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Please answer (a) and (c) only, in typefont and explain each step. Thank you!

Let f : X → Y, A¡ C X for all i e I and B; C Y for all j e J where I and J are some nonempty index sets. Prove the following statements. (a) f (Uier Ai) = Uier f(A;); (b) ƒ (Niei Ai) C Nier S(A;); (c) f- (Njej B;) = Njess(B;). Why wouldn't a set equality hold for part (b)? Explain.
Transcribed Image Text:Let f : X → Y, A¡ C X for all i e I and B; C Y for all j e J where I and J are some nonempty index sets. Prove the following statements. (a) f (Uier Ai) = Uier f(A;); (b) ƒ (Niei Ai) C Nier S(A;); (c) f- (Njej B;) = Njess(B;). Why wouldn't a set equality hold for part (b)? Explain.
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