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I am confused interpreting the statement of this question:

"If L is a regular language then also is the language $L1 = \{ w \in L | w \in L^R \}$?"

Should the symbol "|" (such as) be understood as an logical and?

The language L1, so, would be $ L \cap L^R $ - a subset of L?

Or should the symbol "|" be understood as an logical or?

The language L1, so, would be $ L \cup L^R $?

In both cases it is regular (I believe), since the languages $L$ and $L^R$ are regular, and the union or intersection will be also regular.

Am I understanding this right?

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The notation $L_1 = \{ w \in L \mid w \in L^R \}$ means "the collection of all $w \in L$ that satisfy the condition $w \in L^R$". In other words, $L_1 = L \cap L^R$.

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