Study the diagram given below and answer each of the following questions. How…

Concept

In a three-set Venn diagram, each enclosed region represents one exact combination of set memberships. A phrase like “X and Y but not Z” always points to the region shared by exactly the two shapes X and Y, drawn so that it lies entirely outside the third shape — not any larger or adjacent region that also touches Z.

Application

In this diagram the triangle marks people who take tea, the circle marks people who take coffee, and the rectangle marks people who take wine. The overlap of the triangle and the circle that lies completely outside the rectangle contains 7 — so exactly 7 persons take both tea and coffee but not wine.

Contrast with the other options

• The value for “tea and coffee” without excluding wine-takers is larger, because it also picks up the region shared by all three drinks — that total is too big for what this question asks.

• The value shared by the triangle and the rectangle (tea and wine) belongs to a completely different pair of shapes and does not touch the circle at all.

• The values that sit inside only one shape (tea alone, or coffee alone, or wine alone) don't involve any overlap between tea and coffee, so none of them can answer this question.

Hence the number of persons who take both tea and coffee but not wine is 7.