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to poke (repeatedly, lightly); to nudge
to peck at (one's food); to pick at
to peck at (someone's faults, etc.)
to egg on; to put up to
子どもが棒でアリの巣を突っついて遊んでいた。
The child was playing by poking an ant nest with a stick.
箸で料理を突っつくだけで食べようとしない。
He just pokes at the food with chopsticks and makes no effort to eat.
隣の席の友人が肘で私を突っついて合図した。
The friend next to me nudged me with an elbow to signal.