Question:easy

Which one of the following options is not a property of Boolean Algebra?
Note: + is OR operation, . is AND operation, and ′ is NOT operation

Show Hint

Remember the complement laws precisely: ANDing a variable with its complement gives 0, while ORing a variable with its complement gives 1. Match each option against these two rules.

Updated On: Aug 3, 2026

𝑎+ 𝑏= 𝑏+ 𝑎
𝑎 . 𝑎′ = 1
𝑎+ 𝑎′ = 1
𝑎 . 𝑏= 𝑏 . 𝑎

Show Solution

The Correct Option is B

Solution and Explanation

A quick way to test a Boolean identity is to substitute the two possible values of $a$, namely 0 and 1, and check both cases.

Testing $a.a prime = 1$: If $a=1$, then $a prime = 0$, so $a.a prime = 1.0 = 0$. If $a=0$, then $a prime = 1$, so $a.a prime = 0.1 = 0$. In both cases the result is 0, never 1. So the statement $a.a prime = 1$ is false in general and cannot be a law of Boolean Algebra.

Checking the remaining options: $a+b=b+a$ and $a.b=b.a$ simply swap operand order in OR and AND, which never changes the output of a symmetric operation, so both hold for every combination of $a$ and $b$. The identity $a+a prime = 1$ can be tested the same way: for $a=1$, $a+a prime = 1+0=1$; for $a=0$, $a+a prime = 0+1=1$. It always holds.

Since every option except $a.a prime = 1$ checks out for all input combinations, the option that fails is $a.a prime = 1$, matching the correct law $a.a prime = 0$.

Final answer: Option (B).

Was this answer helpful?

Questions Asked in GATE CS exam

A database has 25,000 fixed-length records of 100 bytes (primary key 15 bytes). The data file is block-aligned so each record is fully contained within a block. The file is indexed by a primary index file, also block-aligned and ordered. Block size is 1024 bytes and a block pointer is 5 bytes. Each index entry stores the block’s anchor key (15 bytes) and a pointer (5 bytes). Binary search on an index file of $b$ blocks needs $\lceil \log_2 b \rceil$ block accesses in the worst case. Given a key, the number of block accesses required to identify the data file block that may contain the record, in the worst case, is ____________.

GATE CS - 2023
Database Management Systems

View Solution

Consider the table Student with attributes (rollNum, name, gender, marks). The primary key is rollNum. The SQL query is:

SELECT *
FROM Student
WHERE gender = 'F' AND marks > 65;

The number of rows returned by this query is:

GATE CS - 2023
Database Management Systems

View Solution

Consider the syntax-directed translation with non-terminals N, I, F, B and the rules:

\[ \begin{aligned} N &\to I\ \#\ F \qquad && N.val = I.val + F.val \\ I &\to I_1\ B \qquad && I.val = 2 \times I_1.val + B.val \\ I &\to B \qquad && I.val = B.val \\ F &\to B\ F_1 \qquad && F.val = \tfrac12 \big(B.val + F_1.val\big) \\ F &\to B \qquad && F.val = \tfrac12 B.val \\ B &\to 0 \qquad && B.val = 0 \\ B &\to 1 \qquad && B.val = 1 \end{aligned} \] Find the value computed for the input string 10#011 (rounded to three decimals).

GATE CS - 2023
Database Management Systems

View Solution

Consider a sequence $a$ of elements $a_0=1,\,a_1=5,\,a_2=7,\,a_3=8,\,a_4=9,\,a_5=2$. The following operations are performed on a stack $S$ and a queue $Q$, both initially empty. [I:] push the elements of $a$ from $a_0$ to $a_5$ (in that order) into $S$.
[II:] enqueue the elements of $a$ from $a_0$ to $a_5$ (in that order) into $Q$.
[III:] pop an element from $S$.
[IV:] dequeue an element from $Q$.
[V:] pop an element from $S$.
[VI:] dequeue an element from $Q$.
[VII:] dequeue an element from $Q$ and push the same element into $S$.
[VIII:] Repeat operation VII three times.
[IX:] pop an element from $S$.
[X:] pop an element from $S$.

GATE CS - 2023
Programming and Data Structures

View Solution

Which one of the following options is not a property of Boolean Algebra?Note: + is OR operation, . is AND operation, and ′ is NOT operation

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Digital Logic

Questions Asked in GATE CS exam

Which one of the following options is not a property of Boolean Algebra?
Note: + is OR operation, . is AND operation, and ′ is NOT operation