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

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28 Feb 2018

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Wilfrid Laurier University

MA121

Introduction to Mathematical Proofs

Fall 2017

Term Test 1

Prof: Robert John Rundle

Midterm Addition

Exercises

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.