The periodic table of Boole

false	a && b	a && !b	a	!a && b	b	a != b	a \|\| b
0	0	0	0	0	0	0	0
0	0	0	0	1	1	1	1
0	0	1	1	0	0	1	1
0	1	0	1	0	1	0	1
true	!a \|\| !b	!a \|\| b	!a	a \|\| !b	!b	a == b	!a && !b
1	1	1	1	1	1	1	1
1	1	1	1	0	0	0	0
1	1	0	0	1	1	0	0
1	0	1	0	1	0	1	0

Formula:

Here are some fun formulas to try: !(a && b) (a || b) && !(a && b) a ? b : true