3.2 Statements & Negations 117 Negating a Statement Involving Or Use a set diagram to visualize the negation of the statement. Then, describe how the original statement can be false. Oregon Treaty 1846 Mexican Cession 1848 Gadsden Purchase 1853 Alaska Purchase 1867 British Cession 1818 This summer I will visit the region acquired by the Oregon Treaty or the Louisiana Purchase. Louisiana Purchase 1803 The United States purchased or annexed its land (outside the original 13 colonies) in 10 stages. Treaty of Paris 1783 Original 13 colonies Texas Annexation 1845 Florida Treaty 1819 Hawaii Annexation 1898 1783: 1803: 1818: 1819: 1845: 1846: 1848: 1853: 1867: 1898: Treaty of Paris Louisiana Purchase British Cession Florida Treaty Texas Annexation Oregon Treaty Mexican Cession Gadsden Purchase Alaska Purchase Hawaii Annexation SOLUTION Start by drawing a set diagram. Identify the regions represented by the original statement. Then identify all the regions other than those represented by the original statement. Original Statement Negation of Statement Places visited Places visited Visit Oregon Treaty region Visit Louisiana Purchase region The original statement is true if you visit one or both of the regions. Visit Oregon Treaty region Visit Louisiana Purchase region The negation of the statement is true if you do not visit either region. Notice that the original statement is still true if you visit both regions. Checkpoint Help at Use a set diagram to visualize the negation of the statement. Then describe how the original statement can be false. I am going to write about the Mexican Cession, the Gadsden Purchase, or the Texas Annexation for my term paper in American History. Copyright © Larson Texts, Inc. All rights reserved.