The correct option is B False
Active and passive are two voices of a sentence.
When the sentence is in active voice, the subject does an action.
When the sentence is in passive voice, the subject receives an action.
(The subject is the noun or pronoun that does/receives an action, indicated by a verb.)
The given sentence is in the active voice, because the subject here, "the cat" does the action "killed".
The given statement is hence false, and option B is correct, A is incorrect.
Had it been in passive voice, the sentence would be:
The pigeon was killed by the cat.
Here the subject 'pigeon' receives the action 'was killed'.