An
oxymoron is a figure of speech in which two words or phrases with contradictory (opposite) meanings are combined in a way that does not make sense, or - more often - does not seem to make sense, although the deeper meaning is logical. The following are oxymorons:
-Deafening silence.
-Mournful optimism.
-Click the start button to shut down (illogical. This is the famous Windows oddity!)
-He gets home fast who drives slowly (logical in the sense that if you drive slowly you will get home safely, unlike someone who drives fast and is likely to have an accident. The latter will get home much later (if ever...), because he/she will have to spend some time in hospital first).
You can see a long list of oxymorons
here. Quite a few of them are funny. Many of them deviate from my understanding of an oxymoron, though.
Note: in the stricter sense, an oxymoron always contains only seemingly contradictory terms, the deeper meaning always being logical.
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A
palindrome is simply a word, phrase or sentence that sounds the same whether you read it from beginning to end or from end to beginning (whether left to right or right to left). Intermediate spaces, punctuation, apostrophes etc. don't count:
-Refer
-Level
-Madam, I'm Adam (madamimadam).
-A
man, a plan, a canal, Panama! (amanaplanacanalpanama)
-Won't lovers revolt now? (wontloversrevoltnow)
Now read them again, this time from right to left.
An extensive list of palindromes can be seen
here.
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Some of the above examples were taken from dictionaries.