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I understand that $\phi$ is a null symbol.
why concatenation of any language L with $\phi$ is $\phi$ rather than L ?

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marked as duplicate by Hendrik Jan, xskxzr, Community Mar 23 at 14:03

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    $\begingroup$ Try using the definition of concatenation. $\endgroup$ – Yuval Filmus Mar 23 at 9:44
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Let us check the definition.

For two sets of strings $S_1$ and $S_2$, the concatenation $S_1\cdot S_2$ consists of all strings of the form $vw$ where $v$ is a string from $S_1$ and $w$ is a string from $S_2$, or formally $S_1\cdot S_2 = \{ vw : v \in S_1, w \in S_2 \}$.

What about $\emptyset\cdot R$?

Since there is no string in the empty set, we cannot find any string of that form $vw$ where $v$ is a string from the empty set. For example, you cannot form a mixed double in tennis if there is no male players. So $\emptyset\cdot R=\emptyset$.

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You're probably confusing $\emptyset$, the langauge that contains no strings at all, with $\{\varepsilon\}$, the language that contains only the empty string.

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