A implies B, B is true, therefore A is true.
This is one of 13 logical fallacies noted by Aristotle and termed as the affirmation of the consequent (B being the consequent, with A as its antecedent).
It looks like obvious logic, but it isn't. Say we have the statement:
"If you're skipping class in the afternoon, you'll be in your room. If you're in your room in the afternoon, you must be skipping class."
Wrong. This kind of logic is faulty on the basis that it does not allow room for other variables such as the cancellation of class or a person's class schedule.
Let's have another go:
"When we lower educational standards, the quality of television shows decreases. If the quality of television shows becomes worse over the next few years, it means educational standards are still lacking."
Again, wrong. There are all kinds of other explanations for the decrease in quality when it comes to television - tampering in creative decisions by network bosses, sloppy production work, poor acting, etc.
The truth:
A implies B, B is true, therefore you cannot say anything about A.
Of course, this is still a very pervasive misconception in our society today, which just sucks because it gives rise to all kinds of misleading assumptions, for instance: "When someone is cold and aloof, they generally keep quiet in front of you. When someone is keeping quiet in front of you, they are cold and aloof."
The truth:
Someone could be shy, suffering from past trauma or preoccupied.
Our society would really benefit from the cleansing of this misconception, don't you think?
P.S.:
See if you can spot the affirmation of the consequent in this table:
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