Chapter 0: Q23P (page 1)

Let it $B$ be any language over the alphabet $\sum$ . Prove that $B = B + i f f B B \subseteq B$

Short Answer

Expert verified

Thus, the solution is $x_{1}, x_{2}, x_{3} \in B$ .

Step by step solution

Introduction

‘B’ is apply to any language over that alphabet $∑$ .

To be confirmation about formula :-

$B = B^{+}$ iff $B B \subseteq B$

Explanation

One Direction: -

Assume: - ^{$B = B^{+}$}----------- result (1)

To Show : - $B B \subseteq B$

Since, forevery language $B B \subseteq B^{+}$ ------- result (2)

By Sabstitating (1) and (2) , it can be obtained that $B B \subseteq B$ . Hence, it’s been confirmed that $B B \subseteq B$ iff role="math" localid="1663234619808" $B B = B^{+}$

Other Direction : -

Assume : - $B B \subseteq B$

To sure and confirmed : - $- B B = B^{+}$

It’s in knowledge in every or any language $B B \subseteq B^{+}$ --------- (3)

Let w be a string of elements, such that $w \in B^{+} w \in B$ .

If $w \in B +$ than W the string can be divided within elements. $x_{1}, x_{2}, x_{3}, . . . . . x_{k} s u c h a s w = x_{1}, x_{2}, x_{3} . . . . x_{k}$ For $x_{1} \in B a n d k ⩾ 1$ .

After long duration $x_{1} x_{2} \in B$ and it is assumed that $B B \in B .$

Same way, it hold for the different elements $x_{3}$ , as well as $x_{3} \in B$ and $B B \subseteq B$ .Thus

$x_{1}, x_{2}, x_{3} \in B$ .

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Let it $B$ be any language over the alphabet $\sum$ . Prove that $B = B + i f f B B \subseteq B$

Short Answer

Step by step solution

Introduction

Explanation

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Let itB be any language over the alphabet ∑. Prove that B=B+iffBB⊆B

Short Answer

Step by step solution

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Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Let it $B$ be any language over the alphabet $\sum$ . Prove that $B = B + i f f B B \subseteq B$