1. One may not set a trap, such as a mouse trap, on Shabbat. The reason is that although one does not actually trap the animal directly in this manner, Chazal were concerned that while setting the trap, an animal may enter it, thus causing the person to violate the biblical prohibition of tzad (Mishnah Berurah 316:18). In contrast, one may set a trap before Shabbat (Yalkut Yosef 316:12), since performing melachah before Shabbat is permitted. One may also open the trap on Shabbat without touching the animal if it gets trapped inside (Shemirat Shabbat K'hilchatah 27:47).

2. Most poskim hold that trapping never applies to people. Thus, there is no halachic issue of trapping that relates to grabbing a toddler who is running away or authorities catching a person attempting to steal or harm others (Piskei Teshuvot 339:7; Shemirat Shabbat K'hilchatah 27, n.119).

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Dedicated by Fran Broder as a zechus for everlasting peace in Eretz Yisrael in the merit of learning Hilchos Shabbos.