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how to Solve Venn Diagrams?

TopVenn diagram expresses the logical relation between various elements of Sets. Venn diagram is the pictorial representation of intersections among sets. Intersection of two sets A and B will be ‘A ∩ B’. Interactions between sets are indicated by circles or ovals, some elements of sets are represented inside the Circle while others are shown outside the circle (oval). Syllogism can be solved in best manner using the concept of Venn diagram. Venn diagrams can be used to show Relations between both finite and infinite sets which may include items or Numbers or objects or matrices etc. In Venn diagram representation, overlapped area indicates the interaction between various elements of sets.

Consider the following example to understand Venn diagrams:

If universal Set U = x: 1≤ x ≤ 10, also set A = 2, 4 and set B = 2, 4, 9.

Then Venn diagram can be drawn as:

Here A ∩ B = 2, 4 and A U B = 2, 4, 9.

Following steps help us to understand how to solve venn diagrams:

1) First of all, identify how many shapes of Venn diagram (circles or ovals) are necessary. For instance, to eat 5 mangoes, five circles or ovals are taken.


2) Circles must be drawn on a plane white paper. Each of the circle must overlap other circle.


3) Name out each of the circle along with name of set and also write the total number of items in that set.


4) Then consider an intersecting part and look it carefully to find the number of elements commonly in both sets.


5) Fill numbers in the remaining shapes and interacting areas. Each part must have a number (zero is also numbered).


6) Add the total number of elements in Venn diagram to be sure that total equals to that amount which is asked in question.