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Given the recursively enumerable language $(L_{RE})$, the context sensitive language $(L_{CS})$, the recursive language $(L_{REC})$, the context free language $(L_{CF})$ and deterministic context free language $(L_{DCF})$. The relationship between these families is given by

  1. $L_{CF} \subseteq​ L_{DCF} \subseteq​ L_{CS} \subseteq​ L_{RE} \subseteq​ L_{REC}$ 
  2. $L_{CF} \subseteq​ L_{DCF} \subseteq​ L_{CS} \subseteq​ L_{REC} \subseteq​ L_{RE}$
  3. $L_{DCF} \subseteq​ L_{CF} \subseteq​ L_{CS} \subseteq​ L_{RE} \subseteq​ L_{REC}$
  4. $L_{DCF} \subseteq​ L_{CF} \subseteq​ L_{CS} \subseteq​ L_{REC} \subseteq​ L_{RE}$
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diagram is showing proper subsets where in options  it is not proper which one is correct
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