Let $\mathit{C}\mathbf{=}\mathbf{\{}\mathit{x}\mathbf{\#}\mathit{y}\mathbf{|}\mathit{x}\mathbf{,}\mathit{y}\mathbf{\in }\left\{0,1\right\}\mathbf{*}\mathit{a}\mathit{n}\mathit{d}\mathit{x}\mathbf{\ne }\mathit{y}\mathbf{\}}\mathbf{.}$Show that$\mathit{C}$ is a context-free language.

The context-free language is generated by context-free grammar. These languages are accepted by Pushdown Automata. These are the superset of regular languages.

Consider context-free languages$L_1$ described as$G_1=(V_1,S,R_1,S_1).$

Consider context-free language$L_2$ described as$G_2=(V_2,S,R_2,S_2).$

Context-free language is a grammar where its language is supports pushdown deterministic automata. Context-free grammar is used to generate context-free languages. A context-free grammar is a formal grammar which is used to generate all the possible patterns of strings in a given formal language. And it is contained number of sets of production rules.

The grammar formed by the given language statement is shown below.

$$\begin{gathered} S\to BL \\ S\to RB \\ L\to BL|A \\ R\to RB|A \\ A\to BAB|\# \\ B\to 0|1 \end{gathered}$$

This grammar follows the property of context-free language or context-free grammar.

Hence, C is a context-free language.