Regular Languages

1. L((a+b)*a)= L(a+b)*
= {a,b}*
= {e,a,b,aa,ab,ba,bb,...}
L((a+b)*a)={a,b}*,{a}
={a,aa,ba,aaa,aba,...}
{w є {a,b}* / w ends in a}
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2 . L(a*b*) = L(a*) L(b*)
L(a*) = {e, a, aa, aaa, aaaa, …}
L(b*) = {e, b, bb, bbb, bbbb, …}
L(a*) L(b*) = {e, a, aa, aaa, aaaa, …}
= {e, b, bb, bbb, bbbb, …}
other option:
if
L(a*b*) = L(a*)L(b*)
L(a*) = {e,a,aa,aaa,....}
L(b*) = {e,b,bb,bbb,....}

then
L(a*)L(b*)={ee,eb,ebb,ebbb,.....,ae,ab,abb,....}
daun sort nimo lexicographic.

therefore ang first five kay:
L(a*)L(b*)={e,a,b,aa,ab}

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3.L(00 + 11) = L(00) U L(11)
= {00, 11}
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4.L(1(0+1)0) = L(1) L(0+1) L(0)
= 1 (L(0)UL(1)) 0
= 1 {0,1} 0
= {100, 110}
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5.L((0+1)* 10(0+1)*) = L((0+1)*) L (10)+ L((0+1)*)
=L(0+1)* L(10) L(0+1)*
=L(0) U L(1)* L(10) (L(0) U L(1))*
=({0} U {1})* {10} ({0} U {1})*
={0,1}* {10} {0,1}*
={e,0,1,...} {10} {e,0,1,...}
={e.10.e,e.10.0,e.10.1,...,0.10.e,0.10.0,0.10.1,...,1.10.e,1.10.0,1.10.1,...}
={10,100,101,010,110,...}
={10,010,100,101,110,...}
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main credits to: NR