Logical Venn Diagrams Questions and Answers

Answer: B

The answer is E, the region inside the square and the circle but outside the triangle.

Players are the square and graduates are the circle, so players who are graduates lie in the overlap of square and circle. That overlap holds two regions, D and E. Region D also lies inside the triangle, which stands for girls, so it is excluded by 'but not girls'. Region E lies outside the triangle and is the one left.

A is a girl only, B is a girl who is a player but not a graduate, and D is a girl who is a player and a graduate.

Answer: D

The answer is the diagram with a circle inside a larger circle and a separate third shape, option (d).

An encyclopaedia is a kind of book, so its set lies entirely inside the set of books. A magazine is neither a book nor an encyclopaedia, so its set stands apart from both.

Option (a) and option (c) make the magazine overlap the books or the encyclopaedias, which is wrong because no magazine is a book. Option (b) shows all three as unconnected, which misses that every encyclopaedia is a book.

Answer: A

The answer is diagram 1, three circles each overlapping the other two.

A person can be a tennis fan, a cricket player and a student all at once, and equally any two of these without the third. Every pair of classes therefore shares members, and the three classes share some members too, which is the three-circle diagram where all circles overlap.

Diagram 2 puts tennis fans and cricket players wholly inside students, which would make every fan and every player a student. Diagram 3 leaves the first and third circles apart, so no tennis fan could be a cricket player or the reverse. Diagram 4 places one class entirely inside another, which is not true of any pair.

Answer: A

The number of artists who are players only is 14.

Artists are the points inside the square and players are the points inside the circle, so artists who are players are in both. 'Only' excludes the doctors, who are inside the triangle. Reading the regions: 8 lies in the square alone, 13 in the circle alone, 6 in the triangle alone, 5 in the circle and triangle, 3 in all three shapes (an artist who is both a player and a doctor), and 10 and 4 in the circle and square but outside the triangle.

\[ 10 + 4 = 14 \]

The distractors come from counting the wrong regions: 10 alone forgets the 4 region below the triangle, 4 alone forgets the 10 region, and 13 is the circle-only region, which holds players who are neither doctors nor artists.

Answer: C

The correct diagram is (C), two separate circles inside one large circle.

Engineers and accountants are both professionals, so each of their circles lies inside the circle for professionals. An engineer is not, as a class, an accountant, and the two groups are treated as separate, so their circles do not overlap.

(A) puts one group outside professionals altogether, (B) shows three unrelated classes, and (D) makes accountants a subset of engineers (or the reverse), which is not their relationship.

Answer: D

The correct figure is (D), two separate circles inside one large circle.

Tables and chairs are both kinds of furniture, so both their circles lie inside the furniture circle. A table is not a chair, so the two inner circles are separate.

(A) makes chairs a kind of table (or the reverse). (B) puts one class outside furniture altogether, and (C) shows a class only partly overlapping furniture, which would mean some tables or chairs are not furniture.