Computer Methods

Math Problem
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Above Venn diagram is made on the base of intersection between three sets, P, Q, R for example "3" is the intersection of all three sets so its is written on the place where all three circle representing the sets, intersect. Similarly "4" and "5" are intersection of sets P, Q and the sets Q,R respectively so these elements are written where this intersection point occurs.


And all the points that are not common in any set are placed in circles where no intersection is occurring.
The relationship between last two predicates is that these define same thing i.e. "Not every lecturer is articulate" does not ever means that " All the lecturer are not articulate" it could mean that "There are some lecturers who are not articulate" so we can not use universal quantifiers for this predicate hence it means that "Not every lecture is articulate but there are some that can be articulate" so in this sense of interpretation last two predicates are same.
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