Final answer:
To write a regular expression for L₁, use 'a{3,}b{0,4}'. For L, use 'a{0,3}b{0,4}'.
Step-by-step explanation:
To write a regular expression for the language L₁ = {aⁿbᵐ, n≥3, m≤4}, we can break it down into two parts:
1. The part that represents n≥3, where 'a' is repeated at least three times. This can be written as 'a{3,}'.
2. The part that represents m≤4, where 'b' is repeated at most four times. This can be written as 'b{0,4}'.
Combining both parts, the regular expression for L₁ is 'a{3,}b{0,4}'.
For the language L = {aⁿbᵐ : n<4, m≤4}, the regular expression can be written as 'a{0,3}b{0,4}'. Here, 'a' can repeat zero to three times and 'b' can repeat zero to four times.