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Question 252218: Let W be all the words in English. A relation L is defined from W to the positive integers that associates each word with the number of letters in the word. For example (L)the = 3 since the word the has three letters.
(a) What pairs in L have second coordinate 1?
(b) Is this relation a function? Explain your answer.
For (b) I do not believe it is, but that's just a wild guess from the little knowledge I know about this topic. Anyone's help on this would be greatly appreciated!
-P.M.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a) Just pick a word that has a length of 1. So any letter will do.
b) Since each word has a specific length (and only ONE specific length), this means that the relation L is indeed a function. If L mapped say the word 'the' to the numbers 3 AND 4 (say hypothetically that 'the' was 3 characters and 4 characters long), then L wouldn't be a function since that input yielded two outputs.
So in general, if every input into the relation yields only one output, then that relation is a function.
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