Q: Sentence (1) You really have to empathize with their doing it.
Sentence (2) You really have to empathize with them.. Word: empathize.
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A: the same meaning

Q: Sentence (1) Hold these truths to be self-evident.
Sentence (2) About a dozen animals were held inside the stockade.. Word: hold.
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A: different meanings

Q: Sentence (1) His claim that he was innocent.
Sentence (2) Evidence contradicted the government's claims.. Word: claim.
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A:
the same meaning