Both sentences S1 and S2 are grammatically incorrect due to the misuse of conjunctions. The sentences use both 'since' and 'so', or 'as' and 'so', which is redundant. The correct forms should only use one conjunction for clarity.
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The question is about identifying the grammatically correct sentences from the given options, so let's evaluate each sentence carefully:
S1: "Since it is raining, so I am not going to play outside."
In this sentence, the use of both "since" and "so" is redundant. Both words act as conjunctions to show cause and effect, and using them together is incorrect. The correct sentence should be "Since it is raining, I am not going to play outside." or "It is raining, so I am not going to play outside."
S2: "As she was ill, so she could not join us for the dance class."
Similar to S1, this sentence incorrectly uses both "as" and "so" together. The correct structure would use just one of them. The sentence should be "As she was ill, she could not join us for the dance class." or "She was ill, so she could not join us for the dance class."
Based on this analysis, neither S1 nor S2 is grammatically correct as they are originally written. Therefore, the correct choice is:
A) Neither S1 nor S2