You have enough to worry about memorizing without keeping dozens of symbols in your head at once. We intend to provide this table for your reference during every in-class evaluation.

Concept	Java/C	Python	This class	Bitwise	Other
true	true	True	\top or 1	-1	T, tautology
false	false	False	\bot or 0	0	F, contradiction
not P	!p	not p	\lnot P or \overline{P}	~p
P and Q	p && q	p and q	P \land Q	p & q	P Q, P \cdot Q
P or Q	p || q	p or q	P \lor Q	p | q	P + Q
P xor Q	p != q	p != q	P \oplus Q	p ^ q	P ⊻ Q
P implies Q			P \rightarrow Q		P \supset Q, P \Rightarrow Q
P iff Q	p == q	p == q	P \leftrightarrow Q		P \Leftrightarrow Q, P xnor Q, P \equiv Q

Concept	Symbol	Meaning
equivalent	\equiv	A \equiv B means A \leftrightarrow B is a tautology
entails	\vDash	A \vDash B means A \rightarrow B is a tautology
provable	\vdash	A \vdash B means both A \vDash B and I know B is true because A is true \vdash B (i.e., without A) means I know B is true
therefore	\therefore	\therefore A means both \vdash A and A is the thing we wanted to show