Conjunction

Let $p$ and $q$ be propositions. The conjunction of $p$ and $q$, denoted by $p\wedge q$, is the proposition that "$p$ and $q$".

$$v(A\wedge B)=\{\begin{array}{ll}1,& \text{if }v(A)=1\text{ and }v(B)=1\\ 0,& \text{if }v(A)=0\text{ or }v(B)=0\end{array}$$

$p$	$q$	$p\wedge q$
T	T	T
T	F	F
F	T	F
F	F	F

For example:

• Let $p$ be that “Today is Tuesday”.
• Let $q$ be that “It is raining today”.
• $p\wedge q$ is that “Today is Tuesday and it is raining today”.

But in English, $p \wedge q$ and $q \wedge p$ do not always mean the same thing.
- "Bob became sick and he visited the doctor."
- "Bob visited the doctor and he became sick."
 
This can be handled by dynamic conjunctions.