Consider the statement, “For all natural numbers n,n, if nn isprime, then nn is solitary.†You do not need to know whatsolitary means for this problem, just that it is aproperty that some numbers have and others do not.
Write the converse and the contrapositive of the statement,saying which is which. Note: the original statement claims that animplication is true for all n,n, and it is that implication that weare taking the converse and contrapositive of.
Write the negation of the original statement. What would youneed to show to prove that the statement is false?
Even though you don't know whether 10 is solitary (in fact,nobody knows this), is the statement “if 10 is prime, then 10 issolitary†true or false? Explain.
It turns out that 8 is solitary. Does this tell you anythingabout the truth or falsity of the original statement, its converseor its contrapositive? Explain.
Assuming that the original statement is true, what can you sayabout the relationship between the set PP of prime numbersand the set SS of solitary numbers. Explain.
