If you sat shiva [mourning] three days before Yom tov, once Yom Tov arrives the laws of shiva are cancelled. [We hold even if you sat shiva for one minute before Yom Tov they are cancelled.]

If it was eight days before Yom Tov, the laws of shiloshim [30 days] are cancelled. Shabbos is included in the count of the shiva.

Moed Katan 3:6

R’ Elazar says since the bais hamikdash was destroyed, Shivuous has the law of Shabbos and is part of shiva. R’ Gamlial says Rosh Hashana and Yom Kippur have the law of Yom Tov and they also nullify the shiva. The Chachamim say Shivuous has the law of Yom Tov and Rosh Hashana and Yom Kippur have the law of Shabbos.