Concern the following axiom set, in which K and L are sets of elements. Axiom A\

Question

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 clement 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 # Phi Does there exist a model of the axiom system A'-F' in which K has exactly 1 element and has at least one element?

Explanation / Answer

the existanxe is a moel of axiom system A'-F' in which K has exactly 1 element and L has at least one element.so 15 and 16 are wrong because Axiom A' is any 2 elements of K belongs to exactly 1 element of L.and Axiom F' is every elementof K belongs to at least 1 element of L.only thease two are satified in 17 th condition.

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