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Must Be True Questions - - Question 33

Leachate is a solution, frequently highly contaminated, that develops when water permeates a landfill site. If and on...

HannahNg February 7, 2020

S & N Statement for If and Only If

I looked at Melody's explanation: "If and only if the landfill's capacity to hold liquids is exceeded does the leachate escape into the environment." #1 "If the capacity to hold liquids is exceeded, then the leachate will escape into the environment." CHLE ==> LEE not LEE ==> not CHLE According to the lesson video, If and Only if introduces N. If it's true, then the statement should be re-written as: LEE ==> CHLE Can sb explain pls? This is the reason why I got wrong.

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shunhe February 7, 2020

Hi @HannahNg,

Thanks for the question! You’ve identified the statement important to figuring out the answer choice here: “If and only if the landfill’s capacity to hold liquids is exceeded does the leachate escape into the environment.” This is a biconditional: the “if and only if” means that we diagram this with arrows in both directions, like the following:

Landfill’s liquid capacity exceeded <—> Leachate escapes into the environment

Which means that if either one happens, the other happens. However, it also means that if either one doesn’t happen, the other one doesn’t happen. In other words, we also know that

~Landfill’s liquid capacity exceeded <—> ~Leachate escapes into the environment

And (E) gives us part of this conditional logic. (E) tells us

~Leachate escapes —> ~Landfill’s liquid capacity exceeded

And this is a statement that directly follows from the biconditional. Thus, (E) is the correct answer. Hope this helps! Feel free to ask any other questions that you might have.