SE 500 Mathematics for Software Engineering
The binary boolean operators

The frequently-used boolean binary operators are as follows: 


 p q |  p=q    p≠q    p∧q   p∨q    p⇒q    p⇐q
-----+------------------------------------------------
 T T |   T      F      T     T      T      T
 T F |   F      T      F     T      F      T
 F T |   F      T      F     T      T      F
 F F |   T      F      F     F      T      T

The sixteen boolean functions with signature Bool × Bool ⟶ Bool are as follows: 
                                                                     f
         t                               n                           a
         r                               a           p      !p   n   l
         u                               n          and     and  o   s
  p q |  e  or  <==  p  ==>  q   =  and  d  !=  !q  !q  !p   q   r   e
 -----+----------------------------------------------------------------------- 
  T T |  T   T   T   T   T   T   T   T   F   F   F   F   F   F   F   F
  T F |  T   T   T   T   F   F   F   F   T   T   T   T   F   F   F   F
  F T |  T   T   F   F   T   T   F   F   T   T   F   F   T   T   F   F
  F F |  T   F   T   F   T   F   T   F   T   F   T   F   T   F   T   F

The four boolean functions with signature Bool ⟶ Bool are as follows: 
                   f
       t           a
       r           l
       u           s
  p |  e  id   ¬   e
 ---+----------------
  T |  T   T   F   F
  F |  T   F   T   F