Venn Diagram | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

A Continuation of Sets

• Venn Diagram is the continuation of sets.
• The same concepts apply here.

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Common Sets

• The Universal set is shown as follows
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  • As mentioned before, it contains all the elements of all the other sets.
• A simple set is drawn as a circle inside the universal set.
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• To show two sets that have no common, or intersection, we show them as follows
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• To show two sets that have a common or intersection, they are drawn as follows
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Coloring of Venn Diagrams

• Do it step by step in the start. It will help you learn how to color in detail.
• Let’s start with something simple. If it says color A’, it means everything other than A. So:
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  • Here the important thing is to realize that the common,
  • This part has A in it, so when we color A prime, we will not color any of it.\

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• Let’s try something more complex. what is we have to color
• Here, we already have colored A’, but we need to determine the common part (intersection part) with B is.
  • Here, you can see the common part between A’ and B. So the final answer will be:

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• • • 
• Let’s try something more difficult. What if we involve a bracket?
  • Here, let’s first solve both bracket.
  • the first bracket we have solved already.
  • Let’s consider what the second bracket will do.
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  • Now, we need to just find the union of both. Union means whatever is present in both of them. So it will end being the same as the above diagram because it contains the part colored in yellow diagram above for the first bracket.
• Let’s try something really hard now, from scratch.
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  • Let’s start with the most complex first bracket.
  • We need to first find C’.
  • 

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• • Now we need to find it’s intersection with A
  • Now we need to find the prime of this all to make it
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  • So it will be as follows, everything other than the previous diagram.
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• • Now let’s do the second bracket First, we need to find B U A
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  • Now we need to find it’s prime, which is everything other than it.
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  • Now we need the common between bracket 1 and 2. So we need the common between:
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  • And
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  • So the final answer is
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• Another situation is the subset one. If A is a subset of B, it can be drawn as follows
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• Remember, once brackets are solved, you have to just go from left to right, even if there are 100 brackets.