Solutions to Truth Functional Expansions

 

  Element    F G H I
a + + +
b + + -
c + - +

 

1)         (x)(Fx Gx)                         False

2)         (x)(Fx (Gx Hx))               False (If not all F's are G's, it can't be the case that all F's are G's and H's)

3)         (x)(Fx (Gx v Hx))               True

4)         (x)(~Ix ~Fx)                       False

5)         (x)(Fx (~Gx v ~Hx))            True (the very element that makes 1 false makes 5 true)

6)         (x)(Gx (Hx ~Ix))                True  (element c)

7)         (x)Fx (y)~Gy                   True

8)         (x)Fx (y)(Gy Iy)             False           

9)         (x)Fx (y)Hy                     True