Homework 7Solving right-linear equations by Arden’s rule:X=PX∪Q=P∗QX=PX\cup Q=P^*QX=PX∪Q=P∗QaC=0C∪1A=0∗1AC=0C\cup1A=0^*1AC=0C∪1A=0∗1AB=0A∪0B∪1C=0A∪0B∪0∗1A=0B∪0A∪0∗1A=0∗(0A∪0∗1A)B=0A\cup0B\cup1C\\ =0A\cup0B\cup0^*1A\\ =0B\cup0A\cup0^*1A\\ =0^*(0A\cup0^*1A)B=0A∪0B∪1C=0A∪0B∪0∗1A=0B∪0A∪0∗1A=0∗(0A∪0∗1A)A=0A∪1B∪λ=0A∪10∗(0A∪0∗1A)∪λ=0A∪10∗0A∪10∗0∗1A∪λ=(0∪10∗0∪10∗0∗1)A∪λ=(0∪10∗0∪10∗0∗1)∗A=0A\cup1B\cup\lambda\\ =0A\cup10^*(0A\cup0^*1A)\cup\lambda \\ =0A\cup10^*0A\cup10^*0^*1A\cup\lambda\\ =(0\cup10^*0\cup10^*0^*1)A\cup\lambda\\ =(0\cup10^*0\cup10^*0^*1)^* A=0A∪1B∪λ=0A∪10∗(0A∪0∗1A)∪λ=0A∪10∗0A∪10∗0∗1A∪λ=(0∪10∗0∪10∗0∗1)A∪λ=(0∪10∗0∪10∗0∗1)∗bB=0D=∅∪0D=0DB=0D=\emptyset\cup0D=0DB=0D=∅∪0D=0DD=1B∪1C∪λ=10D∪1C∪λ=(10)∗(1C∪λ)D=1B\cup 1C \cup \lambda=10D\cup1C\cup\lambda=(10)^*(1C\cup\lambda)D=1B∪1C∪λ=10D∪1C∪λ=(10)∗(1C∪λ)C=0A=∅∪0A=0AC=0A=\emptyset\cup0A=0AC=0A=∅∪0A=0AL(M2)=E(A)∪E(C)=0B∪1C∪0A∪λ=00D∪10A∪0A∪λ=00(10)∗(1C∪λ)∪10A∪λ=00(10)∗(10A∪λ)∪10A∪0A∪λ=00(10)∗10A∪00(10)∗∪10A∪λ=(00(10)∗10∪10)A∪00(10)∗∪λ=(00(10)∗10∪10∪0)∗00(10)∗L(M2)=E(A)\cup E(C)=0B\cup1C\cup0A \cup\lambda\\ =00D\cup10A\cup0A\cup \lambda\\ =00(10)^*(1C\cup\lambda)\cup10A\cup\lambda\\ =00(10)^*(10A\cup\lambda)\cup10A\cup0A\cup\lambda\\ =00(10)^*10A\cup00(10)^*\cup10A\cup\lambda\\ =(00(10)^*10\cup10)A\cup00(10)^*\cup\lambda\\ =(00(10)^*10\cup10\cup0)^*00(10)^* L(M2)=E(A)∪E(C)=0B∪1C∪0A∪λ=00D∪10A∪0A∪λ=00(10)∗(1C∪λ)∪10A∪λ=00(10)∗(10A∪λ)∪10A∪0A∪λ=00(10)∗10A∪00(10)∗∪10A∪λ=(00(10)∗10∪10)A∪00(10)∗∪λ=(00(10)∗10∪10∪0)∗00(10)∗ ABa3. b a 4. bc