Consider the following lists:

$List-I$	$List-II$
$(I)$ $\{x \in[-\frac{2 \pi}{3}, \frac{2 \pi}{3}]: \cos x+\sin x=1\}$	$(P)$ has two elements
$(II)$ $\{x \in[-\frac{5 \pi}{18}, \frac{5 \pi}{18}]: \sqrt{3} \tan 3 x=1\}$	$(Q)$ has three elements
$(III)$ $\{x \in[-\frac{6 \pi}{5}, \frac{6 \pi}{5}]: 2 \cos (2 x)=\sqrt{3}\}$	$(R)$ has four elements
$(IV)$ $\{x \in[-\frac{7 \pi}{4}, \frac{7 \pi}{4}]: \sin x-\cos x=1\}$	$(S)$ has five elements
	$(T)$ has six elements

The correct option is:

• A
  $(I)$ $\rightarrow (P); (II)$ $\rightarrow (P); (III)$ $\rightarrow (T); (IV)$ $\rightarrow (R)$
• B
  $(I)$ $\rightarrow (P); (II)$ $\rightarrow (S); (III)$ $\rightarrow (P); (IV)$ $\rightarrow (S)$
• C
  $(I)$ $\rightarrow (Q); (II)$ $\rightarrow (P); (III)$ $\rightarrow (T); (IV)$ $\rightarrow (S)$
• D
  $(I)$ $\rightarrow (Q); (II)$ $\rightarrow (S); (III)$ $\rightarrow (P); (IV)$ $\rightarrow (R)$