(7) Let p and q and r be the following propositions. p: m/3 is an integer, q: n/2 is an integer, r: (nm)/6 is an integer. Write the following statements using p, q, r and the logical operator symbols V, A, 7,⇒, and ⇒. (a) "Neither m/3 nor n/2 is an integer." (b) "If m/3 is an integer and n/2 is an integer, then (nm)/6 is an integer." (c) "If (nm)/6 is an integer, then m/3 is an integer and n/2 is an integer." This is known as the converse of the statement in (a). Is the statement true or false? Give your reasons. (d) "If (nm)/6 is not an integer, then it is not true that both m/3 and n/2 are in- tegers." This is called the contrapositive of the statement in (a). Is the state- ment true or false? Give your reasons.
(7) Let p and q and r be the following propositions. p: m/3 is an integer, q: n/2 is an integer, r: (nm)/6 is an integer. Write the following statements using p, q, r and the logical operator symbols V, A, 7,⇒, and ⇒. (a) "Neither m/3 nor n/2 is an integer." (b) "If m/3 is an integer and n/2 is an integer, then (nm)/6 is an integer." (c) "If (nm)/6 is an integer, then m/3 is an integer and n/2 is an integer." This is known as the converse of the statement in (a). Is the statement true or false? Give your reasons. (d) "If (nm)/6 is not an integer, then it is not true that both m/3 and n/2 are in- tegers." This is called the contrapositive of the statement in (a). Is the state- ment true or false? Give your reasons.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(7) Let p and q and r be the following propositions.
p: m/3 is an integer,
q: n/2 is an integer,
r: (nm)/6 is an integer.
Write the following statements using p, q, r and the logical operator symbols V, A,
7,⇒, and .
(a) "Neither m/3 nor n/2 is an integer."
(b) "If m/3 is an integer and n/2 is an integer, then (nm)/6 is an integer."
"If (nm)/6 is an integer, then m/3 is an integer and n/2 is an integer." This is
known as the converse of the statement in (a). Is the statement true or false?
Give your reasons.
(d) "If (nm)/6 is not an integer, then it is not true that both m/3 and n/2 are in-
tegers." This is called the contrapositive of the statement in (a). Is the state-
ment true or false? Give your reasons.
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