Our dog died . . . . . . . . old age. A. with B. for C. of D. to

The correct answer is C. of.

The preposition “of” is used to indicate the cause of death. In this case, the dog died of old age.

The other options are incorrect because they do not make sense in the context of the sentence.

• The preposition “with” is used to indicate possession or association. In this case, it would not make sense to say
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  that the dog died with old age.
• The preposition “for” is
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  used to indicate a purpose or reason. In this case, it would not make sense to say that the dog died for old age.
• The preposition “to” is used to indicate a destination or goal. In this case, it would not make sense to say that the dog died to old age.

I hope this helps!