Among $$150$$ faculty members in an institute, $$55$$ are connected with each other through Facebook^® and $$85$$ are connected through WhatsApp^®. $$30$$ faculty members do not have Facebook^® or whatsApp^® accounts. The number of faculty members connected only through Facebook^® accounts is ______________.

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

$$\,\,\,\,\,\,\,\,\,$$$$(i)$$ $$\,\,\,\,\,\,\,\,\,\,$$ Ooty is not a hill-station.
$$\,\,\,\,\,\,\,$$ $$(ii)$$ $$\,\,\,\,\,\,\,\,\,$$ No hill-station can have more than one lake.

In a $$2 \times 4$$ rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?