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First, let's get familiar with the terms: 1. Mixture: A combination of two or more substances that are not chemically combined and can be separated by physical means. 2. Element: A pure substance consisting of only one type of atom. 3. Pure substance: A material with a constant composition, either an element or a compound. 4. Compound: A pure substance formed when two or more different elements combine chemically.

Now, let's analyze each statement based on the definitions above: a. A spoonful of sugar is a mixture. - Sugar is a compound (sucrose) made up of carbon, hydrogen, and oxygen atoms. A spoonful of sugar contains only sugar molecules, so it is not a mixture but a pure substance. b. Only elements are pure substances. - This statement is false because compounds are also pure substances, as they have a constant composition. c. Air is a mixture of gases. - Air is a combination of different gases such as nitrogen, oxygen, and carbon dioxide, which are not chemically combined. So, it is a mixture. d. Gasoline is a pure substance. - Gasoline is a mixture of various hydrocarbon compounds, and its composition may vary. Thus, it is not a pure substance. e. Compounds can be broken down only by chemical means. - Compounds are formed when two or more different elements combine chemically. To separate these elements, a chemical reaction is needed. So, this statement is true.

Based on the analysis in Step 2, we can identify the correct statements: c. Air is a mixture of gases. e. Compounds can be broken down only by chemical means. These are the true statements among the given options.