## How can you prove a language is not regular using closure properties?

Once we have some languages that we can prove are not regular, such as anbn, we can use the closure properties of regular languages to show that other languages are also not regular. L = {w : w contains an equal number of a’s and b’s } a*b* is regular. So, if L is regular, then L1 = L ∩ a*b* is regular.

**What are non regular languages closed under?**

Set of Non-Regular languages is Closed under Complementation operation, But Not closed under Union or Intersection Operation.

- Union Operation : Set of Non-Regular languages is NOT Closed under Union Operation.
- Intersection Operation : Set of Non-Regular languages is NOT Closed under Intersection Operation.

### What do you mean by closure property?

Closure property holds for addition and multiplication of whole numbers. Closure property of whole numbers under addition: The sum of any two whole numbers will always be a whole number, i.e. if a and b are any two whole numbers, a + b will be a whole number. Example: 12 + 0 = 12. 9 + 7 = 16.

**How do you prove not a regular language?**

- The Pumping Lemma is used for proving that a language is not regular. Here is the Pumping Lemma.
- Let L = {0k1k : k ∈ N}. We prove that L is not regular.
- Let L = {(10)p1q : p, q ∈ N, p ≥ q}. We prove that L is not regular.
- There are 3 cases to consider: (a) v starts with 0 and ends with 0.

## Which of the following is non regular?

Discussion Forum

Que. | Which of the following are non regular? |
---|---|

c. | The set of strings in {0, 1}* that encode, in binary, an integer w that is a multiple of 3. Interpret the empty strings e as the number 0. |

d. | None of the mentioned |

Answer:None of the mentioned |

**Are non regular languages closed under concatenation?**

2 Answers. Show activity on this post. You can’t prove it because it isn’t true: the class of non-regular languages isn’t closed under concatenation.

### What is Closure property in discrete mathematics?

Definition: The closure of a relation R with respect to property P is the relation obtained by adding the minimum number of ordered pairs to R to obtain property P. In terms of the digraph representation of R • To find the reflexive closure – add loops.

**What is Closure property in addition?**

Closure Property: The sum of the addition of two or more whole numbers is always a whole number.

## What are closure properties on regular languages?

Closure properties on regular languages are defined as certain operations on regular language which are guaranteed to produce regular language. Closure refers to some operation on a language, resulting in a new language that is of same “type” as originally operated on i.e., regular.

**Is L regular or non-regular language?**

Let’s take some language L which is non regular. Let’s assume compliment of L i.e. $(L^c)$ is regular. Since we know that regular languages are closed under complementation, complementation of $(L^c)$, i.e. $(L^c)^c$ must be regular. Now $(L^c)^c$ is $L$ means $L$ is regular which contradicts the assumption.

### Is the class of non-regular languages closed under intersection?

The class of non regular languages is closed under intersection. How do I solve these two statements using the result above? Any hints would be helpful. Thanks. Know someone who can answer?

**How to prove that L C is not a regular language?**

Since we know that regular languages are closed under complementation, complementation of (L c), i.e. (L c) c must be regular. Now (L c) c is L means L is regular which contradicts the assumption. So, our assumption that L c is regular must be false. Hence, we can prove that L c is not regular.