Final answer:
False, in "The Taming of the Shrew," Katherine and Petruccio engage in a battle of wits and wordplay, but do not fight over the meanings of various words.
True, Petruccio does compare taming Katherine to training a dog.
Step-by-step explanation:
In "The Taming of the Shrew," Katherine and Petruccio do not fight over the meanings of various words. However, they engage in a battle of wits and wordplay throughout the play. Their interactions are filled with clever wordplay, puns, and verbal sparring.
As for whether Petruccio says that taming Kate is like training a dog, this is true. In Act II, Scene 1, Petruccio compares taming Katherine to taming a falcon and training a dog. He believes that marrying her and changing her behavior is similar to teaching a wild animal to be obedient.
Overall, while Katherine and Petruccio engage in a war of words, they do not specifically fight over the meanings of various words. However, their exchanges are filled with verbal challenges and wit.