Which one of the following diagrams is most appropriate to the statement, “Tea-producing places are either in Assam or in Bengal”?
- (a)[FIGURE] One large ellipse with two separate rectangles drawn inside it, side by side; the two rectangles do not touch each other or the ellipse.
- (b)[FIGURE] Two rectangles side by side with a clear gap between them, plus an ellipse straddling the RIGHT-HAND EDGE of the left rectangle — roughly half the ellipse lies inside that left rectangle and the other half projects into the gap. The ellipse does not reach the right-hand rectangle, and the two rectangles do not touch.
- (c)[FIGURE] Two rectangles side by side with a gap between them, plus an ellipse centred ON THE GAP so that it overlaps BOTH rectangles — its left part crosses into the right end of the left rectangle and its right part crosses into the left end of the right rectangle. The two rectangles themselves do not touch.
- (d)[FIGURE] ONE rectangle divided into two halves by a vertical line down its middle, with an ellipse centred on that dividing line and lying wholly inside the rectangle, so that half the ellipse falls in each half of the rectangle.
Answer
Why
Correct — D, (d) the drawing in which a single rectangle is divided down the middle by a vertical line and the ellipse lies wholly inside that rectangle, straddling the dividing line so that half of it falls in each half of the rectangle. Before anything else, a word about what is on the page. The four options of this question are line drawings and carry no text at all: the booklet prints the letters (a) to (d) down the column with a plain black-outline figure of rectangles and ellipses beside each, and nothing in any of the four is labelled — there is no 'Assam', no 'Bengal', no shading and no key. The words that appear in the option list here are a transcription written so that the four drawings can be told apart in print; they are not wording the Commission printed. The reasoning below is about the shapes.
The sentence to be represented is that tea-producing places are either in Assam or in Bengal. Give the rectangles the two States and the ellipse the tea-producing places. The sentence then says two things and only two. First, every tea-producing place lies in one of the two States, so no part of the ellipse may sit outside them. Second, both States are live alternatives, so each ought to contain some part of the ellipse. It says nothing about the whole of either State producing tea, so neither rectangle may be swallowed by the ellipse.
The fourth drawing satisfies exactly that. Its two regions are the two halves of one rectangle, so they share a boundary and leave no space between them, and the ellipse sits wholly inside that rectangle with the dividing line running through it. Every point of the ellipse is therefore inside one half or the other — no tea-producing place is anywhere else — and both halves hold part of it, which is what the two alternatives in the sentence require. The rectangles also extend well beyond the ellipse, leaving room for places in either State that grow no tea, which the sentence permits and does not deny.
Why the others are wrong
- (a)[FIGURE] One large ellipse with two separate rectangles drawn inside it, side by side; the two rectangles do not touch each other or the ellipse. — This drawing turns the containment the other way round. One large ellipse holds two separate rectangles inside it, so if the ellipse is read as the tea-producing places and the rectangles as the two States, the picture says that every place in Assam and every place in Bengal produces tea — which the sentence never claims — and, worse, that there are tea-producing places in the wide region of the ellipse lying outside both rectangles, which the sentence expressly excludes. Reading the roles the other way round does not save it either: if the ellipse were one of the States it could not be a State and a class of places at the same time. A diagram that asserts more than the sentence does is as wrong as one that asserts less, and this one does both at once.
- (b)[FIGURE] Two rectangles side by side with a clear gap between them, plus an ellipse straddling the RIGHT-HAND EDGE of the left rectangle — roughly half the ellipse lies inside that left rectangle and the other half projects into the gap. The ellipse does not reach the right-hand rectangle, and the two rectangles do not touch. — Here the two rectangles stand apart with a clear gap between them and the ellipse straddles the right-hand edge of the left rectangle, so that about half of it lies inside that rectangle and the other half lies in the empty space beyond. The drawing fails on both of the sentence's requirements. Half the tea-producing places are shown outside both States, in territory that belongs to neither, whereas the sentence says they are in one or the other. And the right-hand rectangle contains no part of the ellipse at all, so the second alternative of the sentence would be empty and the statement would have been better written without mentioning it. A candidate who chooses this drawing has probably read the sentence as though it merely said that some tea comes from one of the two States.
- (c)[FIGURE] Two rectangles side by side with a gap between them, plus an ellipse centred ON THE GAP so that it overlaps BOTH rectangles — its left part crosses into the right end of the left rectangle and its right part crosses into the left end of the right rectangle. The two rectangles themselves do not touch. — This is the drawing that has to be rejected carefully, because it gets one thing right. Its two rectangles stand apart with a gap, and the ellipse is centred on that gap so that its left part reaches into the right end of the left rectangle and its right part reaches into the left end of the right rectangle. Both alternatives therefore contain tea-producing places, which is what the sentence wants. But the middle band of the ellipse lies in the gap, inside neither rectangle, and those points are tea-producing places in neither Assam nor Bengal — precisely what the sentence forbids. The whole difference between this drawing and the correct one is whether the two regions touch. Where they touch, as in a single rectangle divided by a line, the union of the two leaves no space unaccounted for; where they do not, any figure spanning both must spill into the gap.
Concept
A logical diagram question asks whether a candidate can hold a sentence and a picture side by side and check that they say the same thing. The regions in the picture stand for classes of things, and three relations between two regions cover almost every categorical sentence. One region wholly inside another says that all of the first are the second — a small circle for doctors inside a large one for graduates says every doctor is a graduate. Two regions overlapping in part say that some of each are the other. Two regions entirely apart say that none of the first are the second. This question needs a fourth construction, the union: when a sentence says that all of one class lies in this class or in that one, the first region must lie inside the two others taken together, with nothing sticking out into unclaimed space. Two properties of ordinary usage decide the rest of the reading. 'Either A or B' in a sentence of this kind is inclusive, so it does not require the two alternatives to be kept apart. And a sentence saying that all of one class lies within another says nothing at all about the second class being exhausted, so a diagram that swallows one region inside the other has added a claim the sentence never made.
Only two questions in this whole paper carry a figure, and both are in this last block; the other is question 118. The Commission uses them to test something no verbal item can reach — whether a candidate can move between a sentence and a picture without losing precision. That is a real official skill, since organisation charts, jurisdiction diagrams and eligibility flow charts all have to be read exactly, and a region that overlaps another by a millimetre in a drawing may represent a class of cases in a department's work. The method that works is mechanical rather than intuitive. Read the sentence and list what it requires and what it forbids. Then take each drawing and ask two questions of it: does it forbid anything the sentence allows, and does it allow anything the sentence forbids. A drawing survives only if the answer to both is no, and on a well-set item exactly one drawing will.
Key facts
- The four options of this question are line drawings printed without any text or labels; only the option letters (a) to (d) appear beside them.
- In a logical diagram, one region lying wholly inside another represents 'all of the first are the second'.
- Two regions overlapping in part represent 'some are', and two regions entirely apart represent 'none are'.
- A sentence of the form 'all X are in A or in B' requires the X region to lie inside the two regions taken together, with no part outside both.
- 'Either A or B' in such a sentence is read inclusively, so a place lying in both alternatives is not excluded by it.
- The sentence does not say that every place in Assam or in Bengal produces tea, so neither State region may be drawn inside the tea region.
- Where two regions share a boundary, as the two halves of a divided rectangle do, their union leaves no unclaimed space between them.
- Where two regions stand apart, any figure spanning both must pass through the gap and so lie partly outside both.
Study next
Common traps
- Reversing the containment, so that the picture says every place in the two States produces tea rather than the other way round.
- Accepting a drawing in which part of the tea region lies outside both State regions, which is exactly what the sentence rules out.
- Reading 'either or' as excluding the overlap, and rejecting a correct drawing because the two alternatives are not kept apart.
- Choosing a drawing that leaves one alternative empty, which makes half the sentence pointless.
- Overlooking whether the two regions touch; the gap between them is the only difference between two of these drawings.
Diagram items are rare in EPFO papers and unmistakable when they appear: the options are pictures and the stem is a single sentence in inverted commas. The family has two members. The first, as here, gives a statement about classes and asks which arrangement of regions represents it. The second gives three named classes — say, doctors, graduates and Indians — and asks which arrangement fits the relations between them. Both are answered by the same discipline of translating the sentence into a list of requirements and prohibitions before looking at any drawing, and by remembering that the arrangement must not add a claim of its own. Candidates lose these items not through faulty logic but by choosing the drawing that looks broadly right and never testing it against the second half of the sentence.
Related PYQs
EPFO_EOAO_2017_Q118Open & attempt →Consider the following figure : [FIGURE: a step-shaped arrow labelled Object on the left, and a vertical hatched line labelled Mirror (Plane) on the right — see figure_note] Which one of the following is the image of the object in the mirror?
- (a) [FIGURE] The same step shape MIRRORED LEFT-TO-RIGHT: the upper horizontal segment is on the RIGHT and its right-hand free end carries the open chevron barb (opening rightwards); the line drops vertically at the left end of that upper segment, then runs LEFT along the lower level and ends in a solid arrowhead pointing LEFT.
- (b) [FIGURE] Exactly the same shape and orientation as the object drawn in the stem: upper horizontal segment on the LEFT with the open chevron barb at its left-hand free end, a vertical drop at its right end, then a lower horizontal running RIGHT and ending in a solid arrowhead pointing RIGHT.
- (c) [FIGURE] The same step shape FLIPPED TOP-TO-BOTTOM, so that it steps UP instead of down: the horizontal segment carrying the open chevron barb at its left-hand free end is now the LOWER one; the line rises vertically at its right end, then runs RIGHT along the upper level and ends in a solid arrowhead pointing RIGHT.
- (d) [FIGURE] The same step shape and the same downward step as the object, but with the two end marks EXCHANGED: the upper horizontal on the LEFT ends in a SOLID ARROWHEAD pointing LEFT, and the lower horizontal on the RIGHT ends in the OPEN CHEVRON barb (opening rightwards).
Answer(a) [FIGURE] The same step shape MIRRORED LEFT-TO-RIGHT: the upper horizontal segment is on the RIGHT and its right-hand free end carries the open chevron barb (opening rightwards); the line drops vertically at the left end of that upper segment, then runs LEFT along the lower level and ends in a solid arrowhead pointing LEFT.
The only other question in this paper whose options are drawings, nine items later — a step-shaped object beside a plane mirror, with the image to be identified.
Practice
- practice — not a real PYQ
Which one of the following arrangements of two regions best represents the statement, 'All accountants are graduates'?
- (a)The region for accountants lies wholly inside the region for graduates
- (b)The region for graduates lies wholly inside the region for accountants
- (c)The two regions overlap in part and each lies partly outside the other
- (d)The two regions lie entirely apart with no common area
Answer(a) The region for accountants lies wholly inside the region for graduates
- practice — not a real PYQ
Which one of the following arrangements best represents the statement, 'All the pens in this box are either blue or black'?
- (a)The region for the pens lies partly outside both the blue region and the black region
- (b)The region for the pens lies wholly within the blue and black regions taken together
- (c)The blue region and the black region both lie wholly within the region for the pens
- (d)The region for the pens lies entirely apart from both the blue region and the black region
Answer(b) The region for the pens lies wholly within the blue and black regions taken together