Consider four events $\text{P, Q, R},$ and $\text{S}$ such that if any of $\text{P}$ and $\text{Q}$ occurs, then either $\text{R}$ occurs or $\text{S}$ doesn’t occur. If exactly one of $\text{R}$ and $\text{S}$ always occurs, which of the following statements is necessarily true? (The notation $\text{E}^{c}$ denotes the complement of the event $\text{E}$).
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$\text{R} \Longrightarrow \text{P}$
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$\text{R} \Longrightarrow \text{P}^{c}$
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$\text{R}^{c} \Longrightarrow \text{Q}^{c}$
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$\text{R}^{c} \Longrightarrow \text{Q}$
