Consider the following argument: If you read a lot, you will become a brilliant conversationalist. If you become a brilliant conversationalist, you will have many friends. Therefore, if you don’t have many friends, you don’t read a lot. Is this a valid argument?
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This is a valid argument, by Modus Tullens twice.
Let p be "one reads a lot". Let q be "one is a brilliant conversationalist". Let r be "one has many friends".
By MT, given "if p then q", or in English, "If one reads a lot, one is a brilliant conversationalist". If ~q, or, "one isn't a brilliant conversationalist", then ~p holds, or "one doesn't read a lot".
By MT for the second pair, and by the same line of logic, if one doesn't have many friends, one isn't a brilliant conversationalist. And by our first line of logic, if one isn't a brilliant conversationalist, one doesn't read a lot.
Therefore, if one doesn't have many friends, one doesn't read a lot.
Obviously in the real world, this could be false, but by the premises given, it is a valid conclusion.