Does A -> B also mean B -> A?

Forums: Statements, Logic, Implications
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I recently got 4 out of 10 logic questions right on an IQ test, so I'd like to improve my reasoning. When doing IQ questions I found this really nice website that often also contains an explanation for the answers. However I don't understand why they one of the answers was selected and this one contains no explanation:

https://i.ibb.co/1q8gMLC/Difficult-logic-question.png

It states four conclusions that could possibly be true. I agree that A is true and D is false. But it seems to me C should be true instead of B.
Because the second statement "Some Ultas are Xanadorans" doens't justify an implication in the other direction, or does it?
Also, if "All Titanians are Ultas" then anything said about Ultas, also applies to Titanians, does it not?

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View best answer, chosen by WouterVos

@WouterVos,

Single arrowhead denotes one way. IF p THEN q and not vice versa.

To answer your question, draw a three circle Venn diagram, T U and X. From first premise, shade out the T who are not U. From the second premise, mark just one individual by a cross in the intersection of U and X ('some'='at least 1')
The diagram indicates that only the first conclusion A and B must be valid because the marked cross need not be in the T circle.

The Venn diagram method is a standard alternative to the use of symbolic logic with 'universal' and 'existential' quantifiers ( (i.e 'all' and 'some')

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@WouterVos,

C is not necessarily true because the group of T that are in U might not be the same as the group of U that is in X. Say Bob is from Titan. That implies that he is also an Ulta. Mary and Sue are also Ultas but not Titans. Mary is also a Xanadoran. That means all the requirements given, all T are in U, some U are in X but this way none of the T are in X so C in not true in this case.

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@WouterVos,

The way I look at it is at the very least some Xanadorans are Ultas - it could be all, but we don't know that from what we have here - so at the very least some Xanadorans are Ultas. So yes C is logical.

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