All X are Y. Some Y are Z. What can be concluded about Some X are Z?

Study for the Logical Reasoning STEM Test. Practice with flashcards and multiple-choice questions, each with hints and explanations. Prepare for success!

Multiple Choice

All X are Y. Some Y are Z. What can be concluded about Some X are Z?

Think in terms of sets and overlaps. All X are Y means every element of X is also in Y (X is contained in Y). Some Y are Z means there exists at least one element that is in both Y and Z. But that element might or might not be one of the elements in X, since X only has to sit inside Y, not cover all of Y. So from these statements you cannot conclude that some X are Z. It could be true if the Y∩Z portion happens to lie inside X, or it could be false if the Y∩Z portion is entirely outside X. That’s why the conclusion is not guaranteed.

Think in terms of sets and overlaps. All X are Y means every element of X is also in Y (X is contained in Y). Some Y are Z means there exists at least one element that is in both Y and Z. But that element might or might not be one of the elements in X, since X only has to sit inside Y, not cover all of Y. So from these statements you cannot conclude that some X are Z. It could be true if the Y∩Z portion happens to lie inside X, or it could be false if the Y∩Z portion is entirely outside X. That’s why the conclusion is not guaranteed.

More practice questions