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
de nitions,
(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 quanti ers, carefully de ning the domain of
de nition and your predicates:
\If a quadrilateral is a rectangle then it has four equal angles ”
(b) Write the
converse
of your quanti ed 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-
ti ed 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 quanti ed
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
^
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT :