Question: 3. Let A,B be o-structures and let h: A B be a o-homomorphism. Prove: (a) h(A) is a universe of a substructure of B. (I

3. Let A,B be o-structures and let h: A B be

3. Let A,B be o-structures and let h: A B be a o-homomorphism. Prove: (a) h(A) is a universe of a substructure of B. (I stated this in class and wrote the main point of the proof without any detail. Reprove this in detail, carefully checking the required conditions. Your proof still shouldn't be more than 4-5 lines.) (b) If o does not have any relation symbols, then h is a o-embedding if and only if it is one-to-one. REMARK: That's why this happens with groups and rings, but not with graphs or orderings. 3. Let A,B be o-structures and let h: A B be a o-homomorphism. Prove: (a) h(A) is a universe of a substructure of B. (I stated this in class and wrote the main point of the proof without any detail. Reprove this in detail, carefully checking the required conditions. Your proof still shouldn't be more than 4-5 lines.) (b) If o does not have any relation symbols, then h is a o-embedding if and only if it is one-to-one. REMARK: That's why this happens with groups and rings, but not with graphs or orderings

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