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

S1: There exists 'S' which satisfies property R + S = S.
S2: There exists 'S' which satisfies property R.S = S

 

A) only S1 is true

B) only S2 is true

C) Both are true

D) Both are false

 

Please answer this with a suitable explanation.
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S1: There exists 'S' which satisfies property R + S = S

Suppose R = anything and S = $(a+b)^{*}$, Then R+S = S

S2: There exists 'S' which satisfies property R.S = S

Suppose R = anything and S = $\varnothing$, Then R.S = S

So both S1 and S2 are true.

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