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 â‰ 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)