From the Internet encyclopedia of philosophy:
“A deductive argument is said to be *valid* if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be *invalid*.”
“In effect, an argument is valid if the truth of the premises logically guarantees the truth of the conclusion”.
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From The Official LSAT SuperPrep:
Sufficient Assumption
“The correct answer (to a sufficient assumption) must, when added to the argument’s explicit premises, result in a conclusive argument; that is, in an argument that fully establishes its conclusion (provided that the explicit premises and the added assumption are all true).”
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Necessary Assumption
“An assumption is a necessary one if it is something that must be true in order for the argument to succeed.”
“To see whether an answer choice is a necessary assumption, suppose that what is stated that answer choice is false. If under those circumstances the prices of the argument fail to support the conclusion, the answer choice being evaluated is a necessary assumption.”
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Putting it all together
For both types of Assumption questions, the stimulus presents an argument that is incomplete and invalid. The correct answer to both types of questions completes the argument, resulting in either a valid or invalid argument.
Sufficient Assumption: creates a *valid* argument when combined with the Evidence and Conclusion from the stimulus.
In other words, combining the Sufficient Assumption with the Evidence from the stimulus generates a Conclusion that must be true.
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Necessary Assumption: when negated, creates an *invalid* argument when combined with the Evidence and Conclusion from the stimulus.
In other words, combining the negation of the Necessary Assumption with the Evidence from the stimulus generates a Conclusion that does NOT have to be true.
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Point of clarification - negating Sufficient Assumption answer choices.
Negating a Sufficient Assumption does NOT create a complete and invalid argument. Rather, such negation merely means the argument remains in its incomplete and invalid form.
Same goes for wrong answer choices for Necessary Assumption. Negating these wrong answer choices merely means the argument remains in its incomplete and invalid form.
Negating a true Necessary Assumption creates a complete and invalid argument. It means that no matter what other information might be discovered, the argument will always be invalid.