Final answer:
The statement that context-free languages are closed under union is indeed true.
Step-by-step explanation:
Context-free languages are closed under union, meaning the union of two context-free languages results in another context-free language. This is formalized by creating a new grammar with a start symbol that can go to either of the original start symbols of the two languages. The statement that context-free languages are closed under union is indeed true. This means that if you take any two context-free languages and form a new language by combining all the strings that are in either one language or the other, this new language will also be context-free.
To illustrate this with an example, imagine two context-free languages — one generated by the grammar G1 and another by the grammar G2. To create a grammar for the union of these languages, you can introduce a new start symbol S and add rules S → S1 | S2, where S1 is the start symbol of G1 and S2 is the start symbol of G2. This way, the grammar for the union will generate all strings that could be generated by either G1 or G2, hence proving the closure property of context-free languages with respect to the union operation.