Since we know logical AND can be expressed with only NOT and OR:

a  b  !a||!b    !(!a||!b)    a&&b     !(a&&b)
0  0     1          0         0          1
0  1     1          0         0          1
1  1     0          1         1          0
1  0     1          0         0          1

Not (A AND B) is equivalent to Not A OR Not B.
So Not A is true if A is false, and Not B is true is B is false.
Therefore, if either A or B is false, Not (A AND B) is true.