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I found the following question

Let G be a grammar with the following productions:
$E→E+T∣T$
$T→T∗F∣F$
$T→(E)∣T−F$
$F→id$
If $LR(1)$ parser is used to construct the $DFA$ using the above productions, how many look-aheads are present for the item $T→.T∗F$ in the initial state?

Now, what I have been doing so far, which I learnt from Ullman, is to add ahead $x$ in production $A->B$ is $x \in first(\beta)$ of $S->\alpha.B \beta \ [x]$. By doing that I get $\$$ to be the only lookahead for the given production but answer given is $T→.T∗F. \{$,+,∗,−}⇒4 $

Am I missing something? How can it be wrong? What's correct way to solve this?

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