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mathlogicvenn-diagram

Logical Venn Diagrams

I have this question :

enter image description here

Unfortunately, my book didn't provide definition and how to draw/read a logic venn diagram, i have to look at the internet but couldn't find any understandable explanation

From what i understand, the logics for the three diagrams are :

  1. X AND NOT (Y OR Z)
  2. NOT X AND (Y OR Z)
  3. Y AND NOT (X OR Z)

Am i right ? Please correct me if i'm wrong

By the ways, does the question mean to combine all three diagrams with OR operation, like :

1 OR 2 OR 3

Any help is greatly appreciated !

Solution

  • I could not understand the question correctly. Here's the logic for the three Venn Diagrams:

    1. Your logic for the first Venn Diagram is correct: X AND NOT (Y OR Z)

    2. Your logic for the second Venn Diagram is slightly incorrect, if you look at the Venn Diagram: It is simply NOT (X) (Everything except X).

    3. In this case as well, the logic is simply Y.

    Now if we perform OR operation on these three:

      (X AND NOT (Y OR Z)) + NOT(X) + Y 
=  X AND NOT(Y) AND NOT(Z) OR NOT(X) OR Y             [By de Morgan's law]

    which matches option c.

    NOTE: Your second and third logics would have been correct if X, Y and Z were the only three regions in the diagram. However there is also a region outside all of them - bounded by the box. You might want to look up on the internet about basics of Venn Diagram, it's one of the easiest things to learn IMO!