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 2 years 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.
 2 years 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.

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KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1So 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?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0n is a prime number

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0n is an odd number

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Almost. 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."

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

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0if n is not a odd number then n is not a prime number or n = 2

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1You'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?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1This 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?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1So if q is "n=2," what is ~q?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1355893931180:dw

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Right. And if r is "n is an odd number," what is ~r?

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0n is not an odd number

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Bingo. 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?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Great. 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."

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0that the answer it was that simple?

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1That was it. Did it all make sense?

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

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0yes but what does it mean by Your answer must contain a conjunction in its premise.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1That 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."

princesspixie
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see thanks so much!!
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