Not (a AND b) is true if either a or b is false.
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.