For each of the following schemata find a nonempty extension

For each of the following schemata, find a non-empty extension for \"H\" that makes the schema true. Take the UD to be {1, 2, 3}. a) (x)((z)Hxz Hxx) b) (x)(y)(Hyy Hxy) c) (x)((y)Hyx (y)Hxy) d) (x)(y)(z)Hyz Hxy)

Solution

Solution:

a) ext of “H” = {<1, 1>}

b) ext of “H” = {<1, 1>, <2, 1>}

c) ext of “H” = {<1, 1>, <1, 2>, <1, 3>,<2, 1>, <2, 2>, <2, 3>,<3, 1>, <3, 2>, <3, 3>}

z = 1

d) ext of “H” : {<1, 1>}