test.py

def cnt(v):
    x, y, z, u, w = bool(v&1), bool(v&2), bool(v&4), bool(v&8), bool(v&16)
    
    return ("T" if 
        (x or y or w) and (z or not w or v) and (not z or not w or not v) and
        len(set([x, y, w])) == 2 and
        len(set([z, not w, v])) == 2 and
         len(set([not z, not w, not v])) == 2
        else "F")
    
    """return ((x or u) + (y or u) + (z or u) + (w or u) + 
           (x or not u) + (y or not u) + (z or not u) + (w or not u) +
           (not x or not y) + (not x or not z) + (not y or not z) +
           (x or not w) + (y or not w) + (z or not w))"""
           
           
def o(v, b):
    return v if b else "\\overline{%s}" % (v,)
        
for j in range(2**2):
    print '&', "$%s \wedge %s$" % (o('u', j&1), o('w', j&2)),
print '\\\\'
print '\\hline'
           
for i in range(2**3):
    print "$" + ' \wedge '.join(o(chr(ord('x') + j), i&(1<<j)) for j in range(3)) + "$",
    for j in range(2**2):
        print '&', cnt(i|(j<<3)),
    print '\\\\'