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Closed Phrase
Any mathematical expression which contains neither a relation symbol nor a placeholder symbol. For example, 2(5  1) is a closed phrase

Open Phrase
any mathematical expression which contains a placeholder symbol, but does not contain a relation symbol. For example, 6 + [3  n] is an open phrase

Closed Sentence
Any mathematical expression which contains a relation symbol, but does not contain a placeholder symbol. For example, 7(4  2) = 13 is a closed sentence.

Open Sentence
Any mathematical expression which contains both a relation symbol and a placeholder symbol. For example, 9 + 2[n  4] > 12 is an open sentence.

