Which of the following is the complement of the boolean function. A'B+CD'+A'B+CD'
(A+B')(C'+D)
The complement of a Boolean expression is obtained with De Morgan's theorems: (X + Y)' = X'Y' and (XY)' = X' + Y'. Equivalently, interchange AND/OR and complement every literal.
Step 1 — Simplify using the idempotent law X + X = X: F = A'B + CD' + A'B + CD' = A'B + CD'.
Step 2 — Apply De Morgan to the sum: F' = (A'B)' · (CD')'.
Step 3 — Apply De Morgan to each product: (A'B)' = A + B' and (CD')' = C' + D.
Step 4 — Hence F' = (A + B')(C' + D).
Check with A = 0, B = 1, C = 0, D = 0: F = 1 (because A'B = 1) and (A + B')(C' + D) = (0 + 0)(1 + 0) = 0, as a complement must give. A'B+CD' is the function itself, not its complement; (A'+B)(C+D') is the dual (only the operators swapped, literals left uncomplemented); AB'+CD' keeps the term CD' uncomplemented, so at C = 1, D = 0 it equals 1 exactly where F also equals 1.
(A+B')(C'+D) option is correct.
Similar Questions
Match the LIST-I with LIST-II
LIST-I
Boolean Algebra LawLIST-II
AxiomsA. Absorption Law I. a+1=1 B. Bounded Law II. a+0=a C. Identity Law III. a*(b+c)=(a*b)+(a*c) D. Distributive Law IV. a+(a*b)=a Choose the correct answer from the options given below:
Consider the Boolean expression given by F=(X+Y+Z)(X'+Y)(Y'+Z).
Which of the following Boolean expressions is/are equivalent to F' (Complement of F)?
A. (X'+Y'+Z')(X+Y')(Y+Z')
B. (XY'+Z')
C. (X+Z')(Y'+Z')
D. (XY'+YZ'+X'Y'Z')
Choose the correct answer from the options given below:
Important Questions from Logic Gates and Boolean Algebra
In Boolean algebra, the term sum of products means
The value of \(\rm \overline{A+B}\) is :
- If A + B = A + C and AB = AC, then which of the following is true?
The Boolean function Y = AB + CD is to be realized using only two-input NAND gates. The minimum number of gates required are:
The minimum number of 2-input NAND gates required to realize the logic function $Y = AB + \bar A \bar B$ is
