Vegetable is related to Animal. Animal is related to Very. Very is related to Air. 
Ancient is related to Myth. Myth is the opposite of Fact. Fact is the opposite of Hypothesis. Hypothesis is the opposite of Essay. 
Vegetable <--RelatedTo--> Animal <--RelatedTo--> Very <--RelatedTo--> Air 
Ancient <--RelatedTo--> Myth <--Antonym--> Fact <--Antonym--> Hypothesis <--Antonym--> Essay 