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Question

Let $'r'$ be a regular expression, then which of the following statements is/are TRUE for every $'r'$?

$\qquad S1: \text{There exists 'x' which satisfies property } r + x =x$.

$\qquad S1: \text{There exists 'x' which satisfies property } r .x =x$.

• A.  $\text{S1 is FALSE, S2 is FALSE}$
• B.  $\text{S1 is FALSE, S2 is TRUE}$
• C.  $\text{S1 is TRUE, S2 is FALSE}$
• D.  $\text{S1 is TRUE, S2 is TRUE}$

Answer 1

I think both the expressions are true

$S1 \Rightarrow$ if you take $x = (\sum)^*$, then $r + x = x$

$S2 \Rightarrow$ if you take $x = \Phi$, then $r .x = x$

Comments

How can both be true simultaneously? Either you can take x as Σ* or take x as a phi

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both are diffrent question so we can take .

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Where is written "simultaneously"?

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Okay

Answer 2

both are true.