# MA121 Study Guide - Midterm Guide: Propositional Calculus, Disjunctive Normal Form, Contraposition

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Wilfrid Laurier University
MA121
Introduction to Mathematical Proofs
Fall 2017
Term Test 1
Prof: Robert John Rundle
Exercises
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MA121 Introduction to Mathematical Proofs
Additional Exercises before Midterm 1 (Fall 2017)
1. Let S be the statement: Every integer that is a multiple of 3 is an even number.
Complete the following sentences.
(a) S is a FALSE statement.
(b) The converse of the statement S is: Every even number is an integer that is a multiple of 3 which
is a FALSE statement.
(c) The contrapositive of S is: Every number that is not even is an integer that is a not a multiple of
3 which is a FALSE statement.
(d) The contrapositive of the converse of the statement S is: Every integer that is a not multiple of
3 is not even number.
(e) The converse of the contrapositive of the statement S is
Every integer that is a not multiple of 3 is not even number
(f) The negation of the statement S is equivalent to:
There is not integer that is a multiple of 3 is an even number.
(g) The negation of the statement S IS NOT equivalent to the statement:
2. Given simple statements:
p
: The integer
kn 3
; where
Zk
;
q
: The integer
mn 2
; where
Zm
:
(a) Write the logical compound statement that underlies the mathematical statement S of Problem 1 above.
qp
(b) Convert each of the mathematical statements in parts (b), (c), (d), (e), (f) and (g) of Problem 1 above
into logical form.
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