Which of the following are binary or unary operations. For those that are not, w

Question

Which of the following are binary or unary operations. For those that are not, where do they fail?

a) x y = 1/x if x is positive S = set of all real numbers
1/(-x) if x is negative

b) x y = xy (concatenation); S = set of all finite-length strings of symbols from the set {p,q,r}

c) x ^ # = [x] where [x] denotes the greatest integer less than or equal to x; S = set of all real numbers

d) x y = min(x,); S = set of all non-negative integers

e) x y = greatest common multiple of x and y; S = set of all non-negative integers

f) x y = x + y; S = the set of Fibonacci numbers

g) x ^ # = the string that is the reverse of x; S = set of all finite-length strings of symbols from the set {p,q,r}

h) x y = x + y; S = set of all real numbers minus the set of all rational numbers

Explanation / Answer

a) Not an operation, fails at x=0.
b) Binary operation.
c) Unary operation.
d) binary operation.
e) binary operation
f) Not an operation. Fails at x = 1, y = 3 (since 4 is not a Fibonacci number).
g) Unary operation.
h) Not an operation. Fails at x = , y = - (since the sum of and - is 0 and 0 is a rational number, hence not in S).

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