How to Solve 2, 3, 4 Statement Syllogism using Venn Diagram

If you want to learn how to solve Syllogism quickly using VENN Diagrams, then let me tell you, you have come to the right place. We will make you learn syllogism quickly and easily. We have both methods of solving syllogism, formulas method and venn diagram method.

Learn How to Solve 2, 3, 4 Statement Syllogism using Venn Diagram

Suppose you are given a 3 statement syllogism like the one given below.

Statements: All the balls are keys. All the keys are bats. Some watches are bats.
1. Some bats are balls.
2. Some watches are keys.
3. All the keys are balls.

how to solve 3 statement syllogism?

This 3 statement syllogism can easily be solved with the help of venn diagrams and also very quickly.
so how to solve this 3 statement syllogism using VENN Diagrams.

Note: if two circles intersect or cuts indicates ‘some’.
one circle in another circle indicates ‘all parts of first comes under second circle’.

lets solve this question with venn diagrams method.
here are the steps
step 1. first draw a circle. write B in it. B means Balls.
step 2. now in the given first statement, since all balls are keys. so draw another circle over this circle concentric to this circle named K (keys) as shown in fig. below.
the above diagram shows that ‘ALL BALLS ARE KEYS’.
step 3. Now see statement 2 which says ‘all the keys are bats’. to represent it, draw another circle over circle named ‘k’ and name it ‘Bats’ as shown in figure below.
The above diagram represents our two statements given in the question above.
all balls are keys.
all the keys are bats.


step 4. Now see 3rd statement which says ‘some watches are bats’. ‘some’ is represented by crossing two circles in venn diagrams. so draw a circle which crosses the ‘bats’ circle like shown in the figure below. Name this circle as ‘W’. ‘W’ is for Watches.
the above diagram represents all the three statements given in the question.
step 5. Now see the first conclusion which says ‘some bats are balls’. Now look at the Venn diagram. Try to find relation (touching of circles) between balls and bats. Since all balls are keys and all keys are bats. So this conclusion is true as there will definitely be some bats which are balls.
so conclusion 1 follows.
step 6. Now see second conclusion which says ‘some watches are keys’. Look at the Venn diagram again. find the relation between watches and keys. As per the diagram and statement, some watches are bats. After looking at the diagram, we see that the circle of watches ‘W’ does not have any touch with circle for keys ‘k’. So it means that there is no relation between watches and keys. So it means conclusion 2 does not follow.
step 7. Now see the third conclusion which says ‘all the keys are balls’. Then take a look at the Venn diagram and try to find the relation between keys and balls. But the diagram and 1st statement both says that ‘all balls are keys’. It means all keys are not balls. Only all balls are keys as given in the statement and shown in the diagram. There can only be ‘some keys are ball’ and not all keys are balls. So this conclusion also does not follows.
So as per Venn diagram method, the answer is ‘only conclusion 1 follows’.
Lets take another example
Statements: Some keys are staplers. Some staplers are posters. All the posters are pens.
1. Some pens are staplers.
2. At least some posters are keys.
3. No poster is key.
4. Some staplers are keys.
first make the venn diagram of the statements above. If you have learned the process of how the venn diagrams should be drawn in the example given above, then you can easily draw the venn diagram of this problem. or otherwise read the full post carefully first.
the venn diagram of this example is shown below.
k is for keys.
s is for staplers.
p is for posters. how to solve syllogism using venn diagram
Now after drawing the venn diagram of the statements given, take a look at the first conclusion which says ‘some pens are staplers’. try to find the relation (touching of circles) between pens and stapler. According to the venn diagram shown above for the given statements, the pens circle cuts the staplers circle means there are definitely some pens which are staplers. So conclusion 1 follows.
now look at the conclusion 2 which says ‘at least some posters are keys’. Take a look at the diagram above. According to diagram, some posters are staplers. The poster circle ‘p’ cuts stapler circle ‘s’ and stapler circle ‘s’ cuts keys circle ‘k’. It means there can be some posters which are keys or there is also a possibility that no poster is key. Since ‘no poster is key’ is third conclusion given. It means either some posters are keys follows or no poster is key follows. Or we can say answer will be ‘either conclusion 2 or conclusion 3 follows’.
Now take a look at the forth conclusion which says ‘some staplers are keys’. This conclusion is statement 1 given in the question and also the diagram clearly represents it because keys circle ‘k’ cuts stapler circle ‘s’. So this conclusion definitely follows.
So overall the answer to above second example is
conclusion 1 and 4 and either 2 or 3 follows.
How to solve 2 or 3 or 4 statement syllogism using venn diagram
Important Note: whenever two conclusions are given as
1. some A are B.
2. No A are B.
and there is some relation between A’s circle and B’s circle as some another circle is between them cutting both circles of A and B. Then the answer is always conclusion ‘either 1 or 2 follows’.
If you like the post, Please Like us on facebook and share this post among your friends.
Thanks a lot for your precious time on the site
This article is originally published by