Consider the following predicates defined by:
M(x; y):
x
has emailed
y;
P(x; y):
x
has called
y
on the telephone,
where universe for
x
and
y
are the students in the MA5801 class. Write the following sentences in terms of these predicates (Note: You may introduce the predicates
x = y
or
x
≠
y
if required).
(a) Peter received a telephone call from Paul.
(b) Steven emailed and telephoned Tom
(c) Russel either emailed or telephoned every student in the class.
(d) Nobody in the class emailed himself/herself.
(e) Every student in the class has either received an email or telephone call from another student in the class.
Prove the statement: "For all integers
n, if
3n + 3
is even, then n is odd"
(Hint: You may need to consider the contrapositive case)