Can you solve these problems based on the given axioms? Problems 15 through 22 c

Question

Can you solve these problems based on the given axioms?

Problems 15 through 22 concern the following axiom set. in which K and L are sets of elements. Axiom A': Any 2 elements of K belong to exactly 1 element of L. Axiom B': No element of K belongs to more than 2 elements of L. Axiom C': No element of L contains all elements of K. Axiom D': Any 2 elements of L contain exactly 1 element of K in common. Axiom E': No element of L contains more than 2 elements of K. Axiom F': Every element of k belongs to at least 1 element of L. Does there exist a model of the axiom system A'-F' in which K = L = phi (the empty set)? Does there exist a model of the axiom system A'-F' in which K = phi and L notequalto phi? Does there exist a model of the axiom system A'-F' in which K has exactly 1 element and L has at least one element?

Explanation / Answer

15 . No

16. No

17. No

Because in axiom A' , there must be at least 2 elements in set K.

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