16.3. Negative Statements http://www.ck12.org
Example A
Use set theory circles to interpret the negation of a disjunction and explain how the negation of a disjunction can be
written in a different way.
Solution:The shaded portion in the box represents the area that is withinPor withinQ. Recall that in mathematical
logic, this is written asP∨Q. In set theory this area is represented similarly asP∪Qwhere the symbol∪stands for
union. While the notation is slightly different, the reasoning about the relationships and implications is identical.
When you negate the statement, you completely switch what is shaded.
A different way to think about this shaded region is that it is the region that isnot inPand also not inQ. This
means that∼(P∨Q)is equivalent to∼P∧∼Q.