TOC/REGULAR EXPRESSION.

Question

in regular expression we use basically 4 operator. that is union, concatenation, kleene star, kleene plus.

when we write regualr expression we use operator and operands.

like a*, a+b, a.b, a+............ here all are string use in expression.

but there is a expression (phi+a);

in this expression we use one empty language with one string . what actually means of that.

Answer 1

L(ϕ+a) = L(ϕ) + L(a) = ϕ U {a} = {a}
 

Here, ϕ means a empty language i.e. a language that doesn't accept empty language.
a means, a language that accepts a single a.

Here, we have a choice means a language which either accepts no string or single occurrence of "a". 

Answer 2

The Regular Expression (∅ + a) means that the finite automaton with input alphabet ∑ = {a} will only accept single 'a'. The ∅ here means empty language (L = {}). TLDR; Regular Expression (∅ + a) is same as a.