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Ullman (TOC) Edition 3 Exercise 3.4 Question 3 (Page No. 122)

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Ullman (TOC) Edition 3 Exercise 3.4 Question 2 (Page No. 122)
Prove or disprove each of the following statements about regular expressions. $(R+S)^{*}=R^{*}+S^{*}$ $(RS+R)^{*}R=R(SR+R)^{*}$ $(RS+R)^{*}RS=(RR^{*}S)^{*}$ $(R+S)^{*}S=(R^{*}S)^{*}$ $S(RS+S)^{*}R=RR^{*}S(RR^{*}S)^{*}$
Prove or disprove each of the following statements about regular expressions.$(R+S)^{*}=R^{*}+S^{*}$$(RS+R)^{*}R=R(SR+R)^{*}$$(RS+R)^{*}RS=(RR^{*}S)^{*}$$(R+S)^{*}S=(R^{*...
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Ullman (TOC) Edition 3 Exercise 3.4 Question 1 (Page No. 121 - 122)
Verify the following identities involving regular expressions. $R+S=S+R$ $(R+S)+T=R+(S+T)$ $(RS)T=R(ST)$ $R(S+T)=RS+RT$ $(R+S)T=RT+ST$ $(R^{*})^{*}=R^{*}$ $(\in+R)^{*}=R^{*}$ $(R^{*}S^{*})^{*}=(R+S)^{*}$
Verify the following identities involving regular expressions.$R+S=S+R$$(R+S)+T=R+(S+T)$$(RS)T=R(ST)$$R(S+T)=RS+RT$$(R+S)T=RT+ST$$(R^{*})^{*}=R^{*}$$(\in+R)^{*}=R^{*}$$(R...
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Ullman (TOC) Edition 3 Exercise 3.4 Question 4 (Page No. 123)
Prove that $(L^{*}M^{*})^{*}=(L+M)^{*}.$Complete the proof by showing that strings in $(L^{*}M^{*})^{*}$ are also in $(L+M)^{*}.$
Prove that $(L^{*}M^{*})^{*}=(L+M)^{*}.$Complete the proof by showing that strings in $(L^{*}M^{*})^{*}$ are also in $(L+M)^{*}.$
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