What are the identity rules for regular expression?

The two regular expression’s P and Q are equivalent (denoted as P=Q) if and only if P represents the same set of strings as Q does.

For showing the equivalence of two regular expressions we need to show some identities of regular expression’s

Let P, Q and R be the regular expressions then the identity rules are as follows −

• εR=R ε=R
• ε*= ε ε is null string
• (Φ)*= ε Φ is empty string
• ΦR=R Φ= Φ
• Φ+R=R
• R+R=R
• RR*=R*R=R+
• (R*)*=R*
• Ε+RR*=R*
• (P+Q)R=PR+QR
• (P+Q)*=(P*Q*)*=(P*+Q*)*
• R*(ε+R)=( ε+R)R*=R*
• (R+ε)*=R*
• Ε+R*=R*
• (PQ)*P=P(QP)*
• R*R+R=R*R