Jan
25
Logical Venn Diagrams
Venn diagrams or logical diagrams are helpful in reasoning type questions. It is useful as a graphics organization tool when comparing two things.
Sets- Universal and Subsets
A set is a collection of elements. For example a, b, c ,d…….x, y, z is the set of English alphabets and all the alphabets are elements. This is known as universal set because it contains all elements but if we take a, e, i, o, u from this set it is known as subset.Here the number of elements in A (Universal set) is 26 and and number of elements in V (subset) is 5.
n(A)=26. n(V) = 5 (n = number of elements)
n(A)=26. n(V) = 5 (n = number of elements)
Let us consider
A= all numbers
B= all odd numbers
C=all even numbers
D= prime numbers
Here A is the universal set contains B, C and D (subsets)
B’=C and C’=B.
B∩D = all odd numbers which are prime (∩ =intersection)
C∩D = only one even number which are prime (e)
The elements which are common to both sets are denoted by intersection and the elements which are in either one or the other set are denoted by union.(∪)
B∩D = all odd numbers which are prime (∩ =intersection)
C∩D = only one even number which are prime (e)
The elements which are common to both sets are denoted by intersection and the elements which are in either one or the other set are denoted by union.(∪)
Let us represent these things in diagrams.
(image from http://mathworld.wolfram.com)
Let us examine different situations represented.
In 1 A, B and Care different sets. For example India Pakisthan and Srilanka.
In 1 A, B and Care different sets. For example India Pakisthan and Srilanka.
In 2 C is a universal set that contains B and A and A is a subset of B. For example Kerala(A), India (B) and Asia (C).
In 3 A and B are different subsets but part of the universal set C India(A) Pakisthan (B)and Asia (C).
In 4 C is universal set that contains A and B which intersects each other in certain points. (A∩B) For example A Boys B Girls A∩B= intelligent C human being.
For more details about Venn diagram click here
A sample Venn diagram:
singers:
Mohanlal, Kishorekumar, Jesudas, S.P.Balasubrahmaniam
Actors:
Kishorekumar, Rajanikanth, Mohanlal, Kamalhassan, Sharukhkhan
Producers:
S.P.Balasubrahmaniam,G.P.Sippy,Mohanlal, Sharukhkhan
Mohanlal, Kishorekumar, Jesudas, S.P.Balasubrahmaniam
Actors:
Kishorekumar, Rajanikanth, Mohanlal, Kamalhassan, Sharukhkhan
Producers:
S.P.Balasubrahmaniam,G.P.Sippy,Mohanlal, Sharukhkhan
Yellow circle: Actors
Blue Circle: Singers
Green Circle: Producers
singers
Mohanlal, Kishorekumar, Jesudas, S.P.Balasubrahmaniam
Actors:
Kishorekumar, Rajanikanth, Mohanlal, Kamalhassan, Sharukhkhan
Producers:
S.P.Balasubrahmaniam,G.P.Sippy,Mohanlal, Sharukhkhan .
Look at the different shades and intersection in the above diagram. We can find
Elements only in “Singers”:Jesudas (1 in blue)
Common elements in “Singers” and “Producers”:S.P.Balasubrahmaniam (1 in blue+green)
Elements only in “Producers”:G.P.Sippy (1 ingreen)
Common elements in “Singers”, “Actors” and “Producers”:Mohanlal(1 in blue+green+yellow)
Common elements in “Singers” and “Actors”:Kishorekumar (1 in blue+yellow)
Common elements in “Actors” and “Producers”:Sharukhkhan (1 in yellow+green)
Elements only in “Actors”:RajanikanthKamalhassan (2 in yellow)
( Oliveros, J.C. (2007) VENNY. An interactive tool for comparing lists with Venn Diagrams.)
A sample question:
which one of the following statements is correct with regard to the above figure.
Only B is all the three shapes.
Only A and B are in all the shapes.
Categories: U.G.C/NET