for a correct answer, 0 for no response, and –1 for an incorrect response.)
a) All functions are surjective.
False
b) The relation R={(1,3), (2,4), (5,7), (6,8)}
True
is transitive.
c) Let f be a bijection from the finite set A to the
True
finite set B. |A| =|B|.
d) If R is a non-empty relation, then so is R
°
R.
False
e) If a relation R is symmetric, it contains an
False
even number of elements.
f) A partial ordering relation must be
True
anti-symmetric.
g) The total number of edges in a complete
False
graph with 5 vertices is 15.
h) All walks are paths.
False
i) There exists a graph G such that the sum of the
False
degrees of its vertices is 9.
j) If f: A
→
B and g: B
→
C are both injections,
True
then g
°
f is as well.
k) If a relation R is symmetric it can not be
False
anti-symmetric.
l) Let [x] and [y] be equivalence classes in an
True
equivalence relation. [x]=[y] or [x]
∩
[y] =
∅
.
m) For 2 relations R and S that are subsets of AxA,
False
R
°
S = S
°
R
n) Let A={1,2,3}. The number of possible
True
relations R
that are subsets of AxA is 2
9
.
o) Let A={1,2,3}. Let R be a relation over AxA
False
such that R={(1,2),(2,1),(3,2)}. R is a bijection.
2) (8 pts) Let R and S be relations that are subsets of AxA. (A={1,2,3,4}. If R={(1,2),
(1,3), (2,4), (3,1), (3,2), (4,4)} and S={(1,4), (2,1), (2,3), (3,2), (4,1), (4,2)}, then what is
R
°
S?
{(1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,3), (3,4), (4,1), (4,2)}