Disjunction

Let $p$ and $q$ be propositions. The disjunction of $p$ and $q$, denoted by $p\vee q$, is the proposition that "$p$ (inclusive) or $q$".

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

$p$	$q$	$p\vee q$
T	T	T
T	F	T
F	T	T
F	F	F

For example: “Students who have taken either maths of physics A-levels are admitted.”

Exclusive OR

$p$	$q$	$p\oplus q$
T	T	F
T	F	T
F	T	T
F	F	F