De Morgan’s Laws:
¬(p∨q)≡¬p∧¬q
¬(p∧q)≡¬p∨¬q
As in a previous exercise, if we use propositional variables, we will not make mistakes while solving this type of exercise.
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- a) Kwame will take a job in industry or go to graduate school
- b) Yoshiko knows Java and calculus
- c) James is young and strong
- d) Rita will move to Oregon or Washington
a) Kwame will take a job in industry or go to graduate school
Let p=”Kwame will take a job in industry” and q=”Kwame will go to graduate school”.
¬(p∨q)≡¬p∧¬q, by the De Morgan Law.
Therefore, the negation of this statement is Kwame won’t take a job in industry, and Kwame won’t go to graduate school.
b) Yoshiko knows Java and calculus
Let p=”Yoshiko knows Java” and q=”Yoshiko knows calculus”.
¬(p∧q)≡¬p∨¬q, by the De Morgan Law.
Therefore, the negation of this statement is Yoshiko doesn’t know Java, or Yoshiko doesn’t know calculus.
c) James is young and strong
Let p=”James is young” and q=”James is strong”.
¬(p∧q)≡¬p∨¬q, by the De Morgan Law.
Therefore, the negation of this statement is James is not young, or James is not strong.
d) Rita will move to Oregon or Washington
Let p=”Rita will move to Oregon” and q=”Rita will move to Washington”.
¬(p∨q)≡¬p∧¬q, by the De Morgan Law.
Therefore, the negation of this statement is Rita won’t move to Oregon, and Rita won’t move to Washington.
Note: When you are negating a compound proposition, always substitute the statements with propositional variables to avoid mistakes.
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