Learn Russian: Книга на полке, а кот на диване. - The book is on the shelf, and the cat is on the sofa.

Полка (shelf) is a feminine noun ending in -а. Because we are talking about a location (where the book is), we use the Prepositional case. For most feminine nouns ending in -а, we drop the -а and add -е, making it на полке.

Does на диване use the same grammar rule as на полке?

Yes! Диван (sofa) is a masculine noun ending in a consonant. To show location in the Prepositional case, we simply add an -е to the end of the word, giving us на диване. Even though полка and диван have different genders, they both take the -е ending in this case.

The English translation says "and the cat", so why does the sentence use а instead of и?

In Russian, а is used to show a slight contrast or a shift in focus, often translated as "whereas" or a contrasting "and". Here, you are comparing the locations of two different things. If you used и, it would sound like you are just making a flat list rather than highlighting the contrast between where the book is versus where the cat is.

Where is the word for "is" in this sentence?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always skipped. You literally say "Book on shelf, whereas cat on sofa." You only need to use a verb for "to be" when you are talking about the past or the future.