combining groups of columns with boolean values to create multiple new columns

Use itertools.product to get the cartesian product of column names then use Series.mul inside a list comprehension to create corresponding column products, finally use pd.concat to concat these products with df:

from itertools import product

l1, l2 = ['A', 'B'], ['X', 'Y']

c = [df[a].mul(df[b]).rename(''.join([a, b])) for a, b in product(l1, l2)]
df = pd.concat([df] + c, axis=1)

Result:

      A      B     X      Y    AX     AY     BX     BY
0  True  False  True  False  True  False  False  False