Match the LIST-I with LIST-II Choose the correct answer from the options given below: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
A-IV, B-I, C-II, D-III
Each Boolean algebra law has a standard defining identity (here * is AND and + is OR).
A. Absorption Law — a term absorbs any product that contains it: a+(a*b)=a, because if a=1 both sides are 1 and if a=0 both sides are 0. A → IV.
B. Bounded Law (null / dominance law) — OR with the upper bound 1 always gives 1: a+1=1. B → I.
C. Identity Law — 0 is the identity element of OR, so a+0=a. C → II.
D. Distributive Law — AND distributes over OR: a*(b+c)=(a*b)+(a*c). D → III.
Every other code fails on at least one pair: A-IV, B-III, C-I, D-II calls the distributive identity the bounded law; A-III, B-IV, C-II, D-I makes distributivity the absorption law; A-II, B-III, C-IV, D-I calls a+0=a the absorption law.
A-IV, B-I, C-II, D-III option is correct.
Similar Questions
Which of the following is the complement of the boolean function.
A'B+CD'+A'B+CD'
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
