First Order Logic

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Homework Statement:
Let sigma = {a,b,c} be a finite alphabet. Construct formulas that specify the following languages over sigma.
Relevant Equations:
sigma = {a,b,c}
An example we were given is as follows: {ua|u∈∑*} (where ∑* is set of all words over ∑) so we have ∀x. last(x) → a(x).

I am given {awa|w∈∑*} to do, and I know that I have to express that a is the first letter and last letter in a word. Could I write it as:
∀x,y ( a(x) ∧ a(y) ∧ x<y → ∃z(x<z<y)), am I on the right track with this, any help would be appreciated, thank you.
 

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