Problems 15 through 22 concern the following axiom set in wh

Problems 15 through 22 concern the following axiom set, in which K and Lare 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 15. Does there exist a model of the axiom system A F\" in which K L (the empty set)? 16. Does there exist a model of the axiom system A\'-F in which K and L o? 17. 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?

Solution

Answer of question (15)

Here there surely exists a model that satisfies given conditions.