College Math

College Math Study Guide

The above shown examples are valid logical arguments. There may be instances when we have quantifiers; that is, the use of ‘some’, ‘there exist’, ‘at least one’ etc. We need to be a little cautious when deriving conclusions from premises with quantifiers. Example 3: Premise 1: Most adults drink wine. Premise 2: Emily is not an adult. Conclusion: Therefore, Emily does not drink wine. Now, in this case, we can draw the following Venn diagram for premise 1.

The gray portion shows those adults who drink wine. Now, for the second premise, we can have two possibilities, as shown here:

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