Active High and Low in Combinational Logic Analysis
For figure (a):
           -z1 = x1 &amp; x2
            z1 = (x1 &amp; x2)' (NAND operation)

For figure (b):
          -z1 = x1 &amp; x2' 
        =&gt; z1 = (x1 &amp; x2')' (Taking complement on both sides)
        

Here &amp; stands for the and operation.

so in order to drive z1 low (i.e., -z1), x2 has to be negated

It is not correct to say an input is negated, instead, we say a LOW on x2 and a HIGH on x1, produces a LOW on z1.
So z1 = x1 NAND x2' in the case of figure (b).