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what is the difference between a chemical symbol and a chemical formula

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A chemical symbol designates an element that belongs to the periodic table.

A chemical formula combines two or more symbols and it represents a chemical compound. We notice that the chemical symbols are followed oftenly by a subscript that represents the mole proprtions of next element.
What is the difference between a chemical symbol and a chemical formula?
A chemical symbol is a code of a chemical element. 
A chemical formula is a mathematical relationship or rule expressed in symbols. 
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