Math & YOU | 3.2 Statements & Negations

3.2 Statements & Negations

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The word "some" means "at least one." In Example 3, there were 4 presidential candidates who won the popular vote, but still lost the election. However, even if there were only one such person, the following statement would be true.

In the United States, some presidential candidates have won the popular vote, but still lost the election.

The set diagram shown in Example 3 is a classic use of a formal Venn diagram. There are two basic sets.

Set A: Candidates who won the popular vote

Set B: Candidates who won the election

These two basic sets determine four regions in the diagram. Moreover, each of the four regions has historical members.
Consumer Suggestion

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Checkpoint Solution

"In the United States, 14 presidents served as vice presidents: J. Adams, Jefferson, Van Buren, Tyler, Fillmore, A. Johnson, Arthur, T. Roosevelt, Coolidge, Truman, Nixon, L. Johnson, Ford, and George H.W. Bush. Of these, Fillmore, A. Johnson, Arthur, and Ford did not win a presidential election."

Here is one way to draw a set diagram showing this information.
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Guest 1 decade ago |

This is a cool Venn diagram. I like how each of the 4 regions have famous people in the region.

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Ron Larson (author)1 decade ago |

Isn't it surprising that you can get more than 50% of the votes in a presidential election and still lose? From what I know of American history, our electoral system is partly based on the fact that many of the founding fathers had skepticism about pure "democracy" and built various checks and balances into the documents that formed America.

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