"Once upon a time when the Alice of Wonderland was a little girl she owned two pets named Tinah and Kinah" I told my son Omar Khayyam and his friend Avicenna. "What kind of pets are they?" asked my son. "Ha ! That's a mystery, Tinah is either a cat or a dog" I answered, "But I won't tell you which, Kinah is also a cat or a dog, But again I won't tell you which."
"Are they same or different?" asked the Avicenna now. "I mean is one of them a cat and the other a dog, or are they both dogs or both cats?"
I replied "It could be that they are the same, or again it could be that they are different"
"I'll bet that they are not both cats," said Omar Khayyam.
"I'll bet Tinah is a cat," said Avicenna.
"Just a minute now," I objected "What is the basis for your guesses?"
"None!" said Omar Khayyam, "but were we right or wrong?"
I thought for a moment. "You know," I said, "It's a funny thing! It so happens that either both of you are right or both of you are wrong, but I won't tell you which !"
From this, the boys were able to deduce whether Tinah is a cat or a dog and whether Kinah is a dog or a cat.
What are they?