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Write the contrapositive of the conditional statement below.
“ n is a prime number implies that n=2 or n is an odd number.”
Your answer must contain a conjunction in its premise.
 one year ago
 one year ago
Write the contrapositive of the conditional statement below. “ n is a prime number implies that n=2 or n is an odd number.” Your answer must contain a conjunction in its premise.
 one year ago
 one year ago

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KingGeorgeBest ResponseYou've already chosen the best response.1
So in general, the contrapositive of the statement (\(\,p\implies q\)) is \((\neg \,q\implies \neg \,p\)). In this case, both your p and q are other sentences. Can you tell me what the "p" is in your conditional statement?
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
n is a prime number
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Right. And the "q"?
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
n is an odd number
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Almost. The "q" in your statement is "n=2 or n is an odd number." Notice that there's an "or" in this statement, so even this can be broken down into something like "q OR r," where q is "n=2", and r is "n is an odd number."
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
So the statement "n is a prime number implies that n=2 or n is an odd number" can be rewritten as \[p\implies (q \vee r)\]
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
if n is not a odd number then n is not a prime number or n = 2
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You're very close, and certainly have the right idea. The contrapositive of \(p\implies (q\vee r)\) is \(\neg(q\vee r)\implies \neg p\). Can you tell me what \(\neg(q\vee r)\) can be rewritten as?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
This is a thing called "De Morgan's Law." It says that \[\neg(q\vee r) \Longleftrightarrow (\neg \,q) \wedge(\neg\,r) \]Can you translate this back into our statements?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
So if q is "n=2," what is ~q?
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
dw:1355893931180:dw
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Right. And if r is "n is an odd number," what is ~r?
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
n is not an odd number
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Bingo. So if we then combine those two statements, ~q AND ~r can be written as "n is not 2, and n is not an odd number." Make sense?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Great. Then the contrapositive of your original statement should be "If n is not 2, and n is not an odd number, then n is not prime."
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
that the answer it was that simple?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
That was it. Did it all make sense?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You almost had it the first time, you just got a little mixed up with the second half of the statement.
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
yes but what does it mean by Your answer must contain a conjunction in its premise.
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
That just means that it has to have "and" somewhere in the statement. So the way it's written, it's fine. If we had written it as "If n is an even integer greater than two, then n is not prime" instead, which says the same thing, it would not be the correct solution because it does not contain "and."
 one year ago

princesspixieBest ResponseYou've already chosen the best response.0
oh i see thanks so much!!
 one year ago
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