To solve this question, the user needs to understand the meaning of the word "while" within the context of the sentence.
The word "while" in this sentence is a conjunction that implies two actions happening at the same time.
Now, let's go through each option and explain why it is right or wrong:
A. True: This option is incorrect. The sentence is not grammatically correct, as it is missing a verb to complete the second part of the sentence. A possible correction would be: "He was cooking dinner while the football match was on TV."
B. False: This option is correct. The sentence is incomplete and has a grammar error. The sentence is not a complete sentence because it is missing a verb to complete the second part of the sentence.
The Answer is: B. False