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To prove that A is a subset of B, you need to show that every element in A appears in B. So you need to find examples of elements of B (letters in girls' names) in which the elements of A appear.

For example, Louise and Amy are girls' names and therefore the letters contained in them = {l,o,u,i,s,e,a,m and y} are elements of B. All elements of A appear in this set so all elements of A are in B ie A is a subset of B.

This works with the English language and AngloSaxon names. Whether or not it does with other languages/cultures I cannot say.

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Q: How do you prove that set A made up of vowels equals a subset of set B which is equal to a letter that appear in a girl's name?
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