how does kate act when she first meets petruchio?

Soon Katharina appears and the others leave Petruchio to woo her. A battle of wits ensues, filled with sexual puns and insults. Petruchio indicates that, whether she wants to or not, he will take her for his wife. Baptista, Gremio, and Tranio join them and Petruchio happily informs the men that he has won Katharina's heart and that the two will be married on Sunday. Katharina snaps back: "I'll see thee hanged on Sunday first." (2.1: 296) Petruchio reassures his companions that Kate and he have agreed that while in public she will remain "curst" though they will be affectionate in private.