Not only I but also David and Iris ______ fond of playing basketball.

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Not only I but also David and Iris ______ fond of playing basketball.

Not only I but also David and Iris ______ fond of playing basketball.
Not only I but also David and Iris ______ fond of playing basketball.

Not only I but also David and Iris ______ fond of playing basketball.
are
not only...but also...连接两个并列主语时,谓语动词要遵循“就近原则”,这里be动词与后面的 David and Iris 保持一致,所以用are.

are not only 。。。but also 从后原则 后面是 David and Iris 两个人 所以要用are

are( be fond of 固定词组‘喜欢’,NOT ONLY ……BUT ALSO ……作主语时谓语动词与BUT ALSO 后面保持一致,即:David and Iris 是复数,故用are

are 就近原则

整句的意思是-----不仅仅是我还有David (戴维)和Iris (爱丽丝)都喜欢打篮球
所以应该是 are