**Example **1: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that,

w contains only a’s or only b’s of length zero or more.

Solution: r = a* + b*

**Example **2: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w is of length one or more and contains only a’s or only b’s. r = a+ + b+

Solution: r = a^{+}+ b^{+}

**Example **3: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w contains zero or more a’s followed by zero or more b’s

Solution: r = a*b*

**Example **4: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w of length even

Solution: r = [(a + b) (a + b)]*

**Example **5: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w of length odd

Solution: r = (a + b) [(a + b) (a + b)]*

**Example **6: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w of length three

Solution: r = (a + b) (a + b) (a + b)

**Example **7: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w of length atmost three

Solution: r = (a + b + ∈) (a + b + ∈) (a + b + ∈)

**Example **8: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w of length odd containing only b’s

Solution: r = (bb)* b

**Example **9: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w starting with a always

Solution: r = a(a + b)*

**Example **10: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w starting and ending with b and having only a’s in between.

Solution: r = b a* b

**Example **11: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w starting and ending with same double letter

Solution: r = {(aa (a + b)* aa) | (bb (a + b)* bb)

**Example **12: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with starting and ending with different letters

Solution: r = (a(a+b)* b) | (b (a + b)* a)

**Example **13: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with at least two occurrence of a

Solution: r = (a + b)* a (a + b)* a (a + b)*

**Example **14: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with exactly two occurrence of a

Solution: r = b* a b* a b*

**Example **15: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with at most two occurrence of a

Solution: r = b* (a + ∈) b* (a + ∈) b*

**Example **16: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with begin or end with aa or bb

Solution: r = ((aa + bb) (a + b)*) + ((a + b) * (aa + bb))

**Example **17: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with begin and end with aa or bb

Solution: r = ((aa + bb) (a + b)* (aa + bb)) + aa + bb

**Example **18: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with total length multiple of 3 always

Solution: r = [(a + b) (a + b) (a + b)]*

**Example **19: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w containing total a’s as multiple of 3 always

Solution: r = [b* a b* a b* a b*]*

**Example **20: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with exactly two or three b’s

Solution: r = a* b a* b a* (b + ∈) a*

**Example **21: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with number of a’s even

Solution: r = b* + (b* a b* a b*)*

**Example **22: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w in which b is always tripled

Solution: r = (a + bbb)*

**Example **23: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with at least one occurrence of substring aa or bb

Solution: r = (a + b)* (aa + bb) (a + b)*

**Example **24: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w with at the most one occurrence of sub-string bb

Solution: r = (a + ba)* (bb + ∈) (a + ab)*

**Example **25: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w without sub-string ab

Solution: r = b* a*

**Example **26: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w without sub-string aba

Solution: r = (a + ∈) (b + aa+ )* (a + ∈)

**Example **27: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w in which 3rd character from right end is always a

Solution: r = (a + b)* a (a + b) (a + b)

**Example **28: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w always start with ‘a’ and the strings in which each ‘b’ is preceded by ‘a’.

Solution: (a + ab)*

**Example **29: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w contains atleast one ‘a’.

Solution: (a + b)* a (a + b)*

**Example **30: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w contain atleast two ‘a’s or any number of ‘b’s.

Solution: (a* a b* a b*) + b*

**Example **31: Let Σ = {a, b}. Write regular expression to define language consisting of strings w such that, w contain atleast one ‘a’ followed by any number of ‘b’s followed by atleast one ‘c’.

Solution: a^{+} b* c^{+}