Which of the following are one-to-one, onto, or both?
a. f : Q → Q defined...
Which of the following are one-to-one, onto, or both?
a. f : Q → Q defined by f(x) = x3 + x.
b. f : S → S defined by f(x) = 5x + 3.
c. f : S → S defined by:
?(?) = {
? + 1 ?? ? ≥ 0
? − 1 ?? ? < 0 ??? ? ≠ −10
? ?? ? = −10
d. f : N → N × N defined by f(n)...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an...
Let A = {1, 2, 3, 4, 5, 6}. In each of the following, give an
example of a function f: A -> A with the indicated properties,
or explain why no such function exists.
(a) f is bijective, but is not the identity function f(x) =
x.
(b) f is neither one-to-one nor onto.
(c) f is one-to-one, but not onto.
(d) f is onto, but not one-to-one.
Let
U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
A = {5,...
Let
U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
A = {5, 7, 9, 11, 13},
B = {6, 8, 10, 12, 14},
and
C = {5, 6, 8, 9, 12, 13}.
List the elements of each set. (Enter your answers using roster
notation. Enter EMPTY or ∅ for the empty set.)
(a) Ac ∩ (B
∩ C c)
(b) (A ∪ Bc) ∪
(B ∩ C c)
(c) (A ∪
B)c ∩
C c