Let $L=L\_1∩L\_2$, where $L\_1$ and $L\_2$ are languages as defined below:

$L\_1=\{a^mb^mca^nb^m∣m,n≥0\}$

$L\_2=\{a^ib^jc^k∣i,j,k≥0\}$

Then $L$ is

1. Not recursive
2. Regular
3. Context free but not regular
4. Recursively enumerable but not context free.

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My attempt :

$L\_1$ is CSL(context sensitive language) and $L\_2$ is regular . The intersection of both languages should be CFL(context free language), and

$L= \{a^mb^mc∣m≥0\}$ 

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