GATE CSE 1992 | Question: 02-i

Question

The operation which is commutative but not associative is:

• A. AND
• B. OR
• C. EX-OR
• D. NAND

Comments

@mohit7891 , Refer the following lectures:

1. Associative, Commutative Property

2. Questions on Associative, Commutative Property

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Commutativity and Associativity of Standard Boolean Operations:

Operation	Boolean	Commutative	Associative
AND	$A \cdot B$	Yes	Yes
OR	$A + B$	Yes	Yes
NOT	$\bar{A}$	NA	NA
XOR	$A \oplus B$	Yes	Yes
XNOR	$A \odot B$	Yes	Yes
NAND	$(A \cdot B)'$	Yes	No
NOR	$(A + B)'$	Yes	No
Implication	$A \rightarrow B$	No	No

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Option D

Answer 1

The answer is D.

Remark:

1. Every logic gate follows Commutative law.
2. AND, OR, Ex-OR, EX-NOR follows Associative law also. NAND, NOR doesn’t follow Associative law.

Comments

@chauhansunil20th

The implication is a logic Gate??

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@akash.dinkar12 why not? why even this doubt?

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Boolean laws are defined for the operations not for the logic gates.

Answer 2

Ans is D you can varify it like  ((AB)'C)' = (A(BC)')' are not equivalent for input 011.

Comments

yes option D

Answer 3

NAND gate is commutative but not associative.

 

Answer 4

We get for inputs 001,011,100 and 110 both the NAND  and NOR are not associative

Answer 5

all gates are commutative and associative , only NAND and NOR are commutative but not associative and this can be easily verified too with an example

((AB)'C')' != (A'(BC)')'  //whole meaning changes

Answer 6

Associative law is invalid for Nand and Nor