• 飼かう — to keep (a pet or livestock)
• 飼育しいく — breeding / raising
• 飼養しよう — rearing / keeping
• 飼料しりょう — animal feed
• 飼主かいぬし — pet owner

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飼 is a 会意形声 character: 食 (food) provides meaning, while 司 (to govern) gives sound. It conveys feeding and managing animals, extending to the act of raising pets or livestock responsibly.

犬いぬを 飼かっています。
I have a dog.

動物どうぶつを 飼かうには 責任せきにんが 必要ひつようです。
Keeping animals requires responsibility.