Question

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

• A. 𝑎+ 𝑏= 𝑏+ 𝑎
• B. 𝑎 . 𝑎′ = 1
• C. 𝑎+ 𝑎′ = 1
• D. 𝑎 . 𝑏= 𝑏 . 𝑎

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.

Answer 1

The Correct Option is B

Step 1: Recall the fundamental laws of Boolean Algebra. The commutative laws state that the order of operands does not affect the result of OR and AND operations, that is \(a+b=b+a\) and \(a.b=b.a\). Both of these hold true for every value of \(a\) and \(b\).

Step 2: Recall the complement laws. Complement laws describe what happens when a variable is combined with its own complement (NOT). The OR complement law says \(a+a'=1\), meaning a variable ORed with its complement always gives logic 1. The AND complement law says \(a.a'=0\), meaning a variable ANDed with its complement always gives logic 0, since one of \(a\) and \(a'\) is always 0.

Step 3: Now examine each option. Option \(a+b=b+a\) is the valid OR commutative law. Option \(a.a'=1\) is NOT valid, because the correct identity is \(a.a'=0\), not 1. Option \(a+a'=1\) is the valid OR complement law. Option \(a.b=b.a\) is the valid AND commutative law.

Step 4: Since only \(a.a'=1\) contradicts a genuine law of Boolean Algebra, it is the odd one out.

\[ \boxed{\text{Option (B): } a.a'=1 \text{ is NOT a valid Boolean Algebra property}} \]