Which of the following substitutions are defined? If undefined, explain why. If
ID: 3110962 • Letter: W
Question
Which of the following substitutions are defined? If undefined, explain why. If defined, give the answer after applying substitution:
(a) (x = y (x, y))[x := f(z)]
(b) ((z)(x = y (x, y)))[x := f(z)]
(c) (((x)(f(x) = z f(z) = x)) ((x) (z)))[x := y]
(d) (((y)g(x, y) = f(y, z)) (((x)(p q)) f(y, z) = x))[p := f(x) = y]
(e) ((((p q) r) ((x)(x, y))) ((z)f(x, z) = y))[p := y = g(x)]
(f) (((x)((p q) r)) ((z)f(x, z) = y))[py = g(x)]
(a) (x=y (x, (b) ((yz)(x = y (x,y)))[x := f(z)] : (d) (((w)g(x, y) = f(y, z)) v (((yz)(p q)) f(y, z) = z))[p := f(x) = y]Explanation / Answer
a) Substitutions Defined
b) Substitutions Defined
c) Substitutions not Defined
d) Substitutions Defined
e) Substitutions Defined
f) Substitutions not Defined
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