Question

Activity 10.5.

Suppose A is a set that definitely does not contain any cats, and let

f:P(A)→P(A∪{Grumpy Cat})

represent the function defined by

f(X)=X∪{Grumpy Cat}

(a) Verify that f is injective.

(b)Verify that f is not surjective.

(c) Describe specifically how to restrict the codomain of f to make it bijective.

restricting the codomain

the “induced” function X→B created from function f:X→Y and subset B⊆Y by “forgetting” about all elements of Y that do not lie in B, where B must contain the image of f

(d) Describe the input-output rule for f−1, the inverse function of the bijective version of f from Task c.

Answer 1