3.2 Statements & Negations

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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.
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