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Logic and Sets
Logic and Sets
Discrete mathematics starts with statements, truth values, and collections of objects called sets.
Logical Connectives
- $p \land q$: and
- $p \lor q$: or
- $\neg p$: not
- $p \to q$: if $p$ then $q$
Sets
Common operations are union $A \cup B$, intersection $A \cap B$, and complement $A^c$.
Example 1
If $A=\{1,2,3\}$ and $B=\{3,4,5\}$, find $A \cap B$.
$\{3\}$.
Example 2
What is $A \cup B$ for the same sets?
$\{1,2,3,4,5\}$.
Practice Problems
1. What does $\neg p$ mean?
2. If $A=\{1,2\}$ and $B=\{2,3\}$, find $A \cap B$.
3. Find $A \cup B$ for the same sets.
4. What does $p \land q$ mean?
5. What does complement mean?
Show Answer Key
1. Not $p$
2. $\{2\}$
3. $\{1,2,3\}$
4. Both $p$ and $q$ are true
5. Everything not in the set, relative to the universal set