It turns out that 8 is solitary. Does this tell you anything about the truth or falsity of the original statement, its converse or its contrapositive? Explain. Assuming that the original statement is true, what can you say about the relationship between the set P of prime numbers and the set S of solitary numbers. Explain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the statement, "For all natural numbers n, if n is prime, then
n is solitary." You do not need to know what solitary means for this
problem, just that it is a property that some numbers have and others
do not.
(a) Wte the converse and he contrapositive of the statement,
saying which s which. Mote: the originalstatementlaims that
an implication is true for all n, and it is that implication that we
are taking the converse and contrapositive of.
are taking the conver e and or
(b) Write theMnegation of thegriginal statement. What would you
need to chow to prove that the statement is false?
(Even though you don't know whether0 is solitary (in fact,
nobody knows this), is the statement "if 0 is prime, then 10 is
solitary" true r false? Explain.
(d) It turns out that 8 is solitary. Does this tell you anything about
the truth or falsity of the original statement, its converse or its
contrapositive? Explain.
(e) Assuming that the original statement is true, what can you say
about the relationship between the set P of prime numbers and
the set S of solitary numbers. Explain.
Transcribed Image Text:Consider the statement, "For all natural numbers n, if n is prime, then n is solitary." You do not need to know what solitary means for this problem, just that it is a property that some numbers have and others do not. (a) Wte the converse and he contrapositive of the statement, saying which s which. Mote: the originalstatementlaims that an implication is true for all n, and it is that implication that we are taking the converse and contrapositive of. are taking the conver e and or (b) Write theMnegation of thegriginal statement. What would you need to chow to prove that the statement is false? (Even though you don't know whether0 is solitary (in fact, nobody knows this), is the statement "if 0 is prime, then 10 is solitary" true r false? Explain. (d) It turns out that 8 is solitary. Does this tell you anything about the truth or falsity of the original statement, its converse or its contrapositive? Explain. (e) Assuming that the original statement is true, what can you say about the relationship between the set P of prime numbers and the set S of solitary numbers. Explain.
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