Discrete Mathematics I

MATH/CSCI 2112 Assignment 2 Due 30 Jan 2015
(1) Let
G
represent the set of all T.V. game shows. Let
P
be the set of people in
your neighbourhood. Let
C
(
p; g
) be the predicate that the person
p
appeared
on game show
g
and
D
(
p
) be the predicate the p is a doctor. Using the above
denitions,
(i)
translate: There is a person in your neighbourhood who has
been a contestant on a game show but is not a doctor” into symbolic notation.

(ii)
Negate your symbolic expression (show steps).
(iii)
Finally, translate the
statement from
(ii)
into English.
(2) (a) Express symbolically, using quantiers, carefully dening the domain of
denition and your predicates:
If a quadrilateral is a rectangle then it has four equal angles ”
(b) Write the
converse
of your quantied statement above.
(c) Is the implication true? Is the converse true?
(d) In light of your answers to the last two questions above, express a quan-
tied statement to identify rectangles
(3) Determine whether each statement below is true or false (give a brief expl.
for your answer), and in each case, obtain the negation of the quantied
statement.
(a)
8
a; b
2
R
;
p
ab
=
p
a
p
b
(b)
8
a
2
[0
;
1
)
;
9
x
2
R
such that
x
2
=
a