Alice her father that both she and her husband would be happy if he would live with them.

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(答案→)A. convinced
B. reinforced
C. pledged
D. required
解析：convince sb. +that从句意为使……相信，说服……。
convince sb of sth; I tried to convince them of his innocence. convince sb to do sth; We convinced him to go by car.
convinced adj Be convinced of/that; I am convinced of his guilt./I am convinced that he is guilty. convincing adj令人信服的 
reinforce 加强，增强。pledge发誓，保证.