C241 PLTL SESSION –
11/4/2014
Relations
Warm-Up Exercise
• Grab a worksheet
• Begin completing the worksheet in pairs or small groups
Problem 1
1) All relations are over the set S = {1, 2, 3, 4}.
R = {(1,1), (1,2), (1,4), (2,2), (2,3), (3,3), (3,4), (4,4)}
a. Draw a graph of R, visualized as the four points in S.
b. Draw another graph of R on the xy-plane.
c. Is R symmetric? Is it reflexive?
d. Is R a function?
Problem 2
2) R = {(1,1), (1,2), (1,4), (2,2), (2,3), (3,3), (3,4), (4,4)}
Add the necessary elements to make R symmetric.
Problem 3
3) Define one surjective relation and one injective relation in set
builder notation. Now, add or remove the elements you need to
make both of these relations bijective.
Problem 4 from old PowerPoint
Visit the SETL website, http://setl.org/setl-server.html, and answer the
following questions:
(Give both the answer and the SETL code that generated you this answer.)
Note that sets are denoted by braces {}, the intersection operator for sets is
denoted by *, and the union operator for sets is denoted + in SETL. Using
parentheses, (), to denote a set is a more conventional notation than using
braces, {}.
A = (11, 4, 13, 4, 25, 6, (), (1, 2)), B = (1, 4, 25, 6, (), 17, 8, 9), and C = (4, 7, 8, 9,
10, (11, 12, 13), 12)
(i) What is the set difference between A and B?
(ii) What is the set difference between C and D = (11, 12, 13)?