This is an article excerpted from YOURDICTIONARY.COM
A paradox is a statement that apparently contradicts itself and yet might be true (or wrong at the same time). Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.

One of the most well known examples that teachers frequently use to introduce the idea of a paradox is a "jumbo shrimp." Certainly, "jumbo" and "shrimp" are contradictory statements. However, that is merely an introductory example, since a shrimp can certainly be jumbo sized in comparison to other smaller shrimp. Still, it is an appropriate starting point for students who are new to the concept of paradox.

Here are some more examples of paradox in simple forms in order to further define the term "paradox":
1.) You can save money by spending it.
2.) I'm nobody.
3.) "What a pity that youth must be wasted on the young." - George Bernard Shaw
4.) Wise fool
5.) Bittersweet
6.) "I can resist anything but temptation."-Oscar Wilde
7.) I'm a compulsive liar- am I lying when I say that?
8.) A rich man is no richer than a poor man.
9.) Nobody goes to that restaurant because it is too crowded.
10.) You shouldn't go in the water until you know how to swim.
11.) If you didn't get this message, call me.
12.) The person who wrote something so stupid can't write at all.
13.) Men work together whether they work together or apart. -Robert Frost
15.)Be cruel to be kind
16.)The beginning of the end
17.)Drowning in the fountain of eternal life
18.)Deep down, you're really shallow.