It is given that every element of is in , and that some element of is not in . Which of the following must be true?
Answer and explanation
Correct answer: B. Some element of is not in
- Step 1: Take an element of that is not in . Since every element of is in , is in as well.
- Step 2: So is an element of that is not in : some element of is not in .
Answer
Some element of is not in .
Why not the others: The other statements are not forced: elements of outside , elements of inside , and elements of inside can all exist consistently with the two facts, while 'every element of is in ' directly contradicts them.
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