Explanation:

Context-free languages:
Context-free languages are a class of formal languages that can be described by a context-free grammar. A context-free grammar consists of a set of production rules that define how symbols can be rewritten as other symbols. Context-free languages are used to describe the syntax of programming languages, markup languages, and other formal languages.

Closure properties:
Closure properties refer to the behavior of a class of languages when certain operations are applied to them. In the context of context-free languages, closure properties determine whether the result of applying certain operations to a context-free language is still a context-free language.

Union:
The union of two languages L1 and L2 is defined as the set of strings that are either in L1 or in L2.

Concatenation:
The concatenation of two languages L1 and L2 is defined as the set of strings formed by concatenating a string from L1 with a string from L2.

Intersection:
The intersection of two languages L1 and L2 is defined as the set of strings that are both in L1 and in L2.

Kleene closure:
The Kleene closure of a language L is defined as the set of all possible concatenations of zero or more strings from L.

Explanation of False Statement:

The false statement is option 'C' - "Context-free languages are closed under intersection."

Explanation:
- The intersection of two languages L1 and L2 is defined as the set of strings that are both in L1 and in L2.
- In the case of context-free languages, the intersection operation does not have closure under it.
- This means that if we take two context-free languages L1 and L2, and intersect them, the resulting language may not necessarily be a context-free language.
- In fact, the intersection of two context-free languages can be a language that is not even context-sensitive, let alone context-free.

Example:
Consider two context-free languages:
L1 = {a^n b^n c^n | n >= 0} - the language of balanced parentheses.
L2 = {a^n b^n | n >= 0} - the language of equal numbers of 'a' and 'b'.

- The intersection of L1 and L2 is the set of strings that are both in L1 and in L2.
- However, the intersection of L1 and L2 is the language {a^n b^n c^n | n >= 0}, which is not a context-free language.
- This example demonstrates that the intersection of two context-free languages is not necessarily a context-free language.

Conclusion:
In conclusion, the false statement is option 'C' - "Context-free languages are closed under intersection." The intersection of two context-free languages may not necessarily be a context-free language.