The Truth Tables between two variables, A and B. There are 16 possibilities. I'm comparing the logic notation, the set notation, and the truth table. I'm also pairing each one with its complement.

 

A and B
A∧B
      
logic
¬(A∧B)    or   A→¬B
A∩B
set
(A∩B)′
A
B
AND(A,B)
T
T
T
T
F
F
F
T
F
F
F
F
 
A
B
NAND(A,B)
T
T
F
T
F
T
F
T
T
F
F
T
 
A or B
A∨B
logic
¬(A∨B)
A∪B
set
(A∪B)′
A
B
OR(A,B)
T
T
T
T
F
T
F
T
T
F
F
F
 
A
B
NOR(A,B)
T
T
F
T
F
F
F
T
F
F
F
T
 
A exclusive or B
¬(A∧B)
logic
A↔B
(A∪B)−(A∩B)
set
((A∪B)−(A∩B))′
A
B
XOR(A,B)
T
T
F
T
F
T
F
T
T
F
F
F
 
A
B
XNOR(A,B)
T
T
T
T
F
F
F
T
F
F
F
T
 
name = ??
A∧(¬B)
logic
A→B
A∩B′
set
  
A
B
AND(A,NOT(B))
T
T
F
T
F
T
F
T
F
F
F
F
 
A
B
NAND(A,NOT(B))
T
T
T
T
F
F
F
T
T
F
F
T
     
     
always true
1
logic
0
U
set
∅
A
B
TRUTH(A,B)
T
T
T
T
F
T
F
T
T
F
F
T
 
A
B
FALSE(A,B)
T
T
F
T
F
F
F
T
F
F
F
F
     
     
always A
A
logic
¬A
A
set
A′
A
B
A(A,B)
T
T
T
T
F
T
F
T
F
F
F
F
 
A
B
NOT_A(A,B)
T
T
F
T
F
F
F
T
T
F
F
T
     
     
always B
B
logic
¬B
B
set
B′
A
B
B(A,B)
T
T
T
T
F
F
F
T
T
F
F
F
 
A
B
NOT_B(A,B)
T
T
F
T
F
T
F
T
F
F
F
T
     
     
name = ??
¬A∧B
logic
A∨¬B
A′∩B
set
A∪B′
A
B
AND(NOT(A),B)
T
T
F
T
F
F
F
T
T
F
F
F
 
A
B
OR(A,NOT(B))
T
T
T
T
F
T
F
T
F
F
F
T