How to Analyze Compound Statements

By Mary Jane Sterling

If your finite math instructor asks you to analyze a compound statement, you can try using a truth table to do this. Not every topic in a discussion can be turned into a compound statement and analyzed for its truth that way, but using logic and truth values is a good technique to use when possible.

Consider the compound statement

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When constructing a truth table, you start with the basic p and q columns. Then you add a ~ q column followed by a column

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Before you can perform the conjunction, ^, you need a ~ p column. Here’s a step-by-step procedure.

  1. Start with a basic p and q and then add ~ q.
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  2. When adding the
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    column, perform the disjunction on the first and third columns.
    Remember, with disjunctions, the statement is false only when both component statements are false.
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  3. Add the ~ p column.
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  4. Add the
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    column, which shows the conjunction of the fourth and fifth columns.
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The conjunction is true only when the two component statements are true. This complex statement is only true when both original statements are false.