From the given logic diagram: Derive Boolean expression and draw the truth table for the derived…

From the logic diagram: Gate 1 is a NAND gate with inputs A and B, giving output (1) = $(A.B)'$. Gate 2 is an AND gate with inputs B' and C, giving output (2) = $B'.C$. Gate 3 is an OR gate combining (1) and (2), giving output (3) = $(A.B)' + B'.C$. The final gate is a NOT gate acting on (3), giving output $X = [(A.B)' + B'.C]'$. Truth table:

A	B	C	(A.B)'	B'.C	(A.B)'+B'.C	X
0	0	0	1	0	1	0
0	0	1	1	1	1	0
0	1	0	1	0	1	0
0	1	1	1	0	1	0
1	0	0	1	0	1	0
1	0	1	1	1	1	0
1	1	0	0	0	0	1
1	1	1	0	0	0	1

$X = [(A.B)'+B'.C]'$. For $A=1, B=0, C=1$: $A.B = 1.0 = 0 \Rightarrow (A.B)'=1$. $B'=1 \Rightarrow B'.C = 1.1 = 1$. $(A.B)'+B'.C = 1+1 = 1$. $X = 1' = 0$. Final answer: X = 0