- 2. {(w,n,r,g)}[∃x.man(x)]
-
- = {(w,n+1,r[x->n],g[n->a])}[man(x)] ++ {(w,n+1,r[x->n],g[n->b])}[man(x)]
- = {} ++ {(w,n+1,r[x->n],g[n->b])}
- = {(w,n+1,r[x->n],g[n->b])}
- -- only b is a man
-
- 3. {(w,n,r,g)}[∃x∃y.person(x) and person(y)]
-
- = {(w,n+1,r[x->n],g[n->a])}[∃y.person(x) and person(y)]
- ++ {(w,n+1,r[x->n],g[n->b])}[∃y.person(x) and person(y)]
-
- = ( {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a])}[person(x)][person(y)]
- ++ {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->b])}[person(x)][person(y)])
- ++ ( {(w, n+2, r[x->n][y->n+1], g[n->b][n+1->a])}[person(x)][person(y)]
- ++ {(w, n+2, r[x->n][y->n+1], g[n->b][n+1->b])}[person(x)][person(y)])
-
- = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]),
- (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b])}
- ++ {(w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]),
- (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b])}
-
- = {(w, n+2, r[x->n][y->n+1], g[n->a][n+1->a]),
- (w, n+2, r[x->n][y->n+1], g[n->a][n+1->b]),
- (w, n+2, r[x->n][y->n+1], g[n->b][n+1->a]),
- (w, n+2, r[x->n][y->n+1], g[n->b][n+1->b])}
-
- -- there are four ways of assigning x and y to people