GATE CSE 2024 | Set 2 | Question: 20

Question

​​​​For a Boolean variable $x$, which of the following statements is/are FALSE?

• A. $x .1=x$
• B. $x+1=x$
• C. $x \cdot x=0$
• D. $x+\bar{x}=1$

Comments

Video Explanation: https://youtu.be/DbKnUyyzlZs?t=3753

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i made mistake in identity law. i took it as a boolean expression.

 

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Option B,C

Answer 1

•  $x.1=x$ identity law. it is true.
• $x+1=x$ it is false. it should be $x+1=1$
• $x.x=0$ it is false, it should be $x.x=x$
• $x+\bar x=1$ complement law. it is true

So option $(B,C)$ is false here.

Comments

for this type of true false just read all law and logic gate clearly and know reason then this type true false is easy.

Answer 2

In this question, Boolean algebra will be used:

•  + means OR
•  . means AND
• x̄ means Complement

1. 𝑥.1=𝑥 identity law. it is true.
2. 𝑥+1=𝑥, it should be 𝑥+1=1 (Anything OR 1 is 1)
3. 𝑥.𝑥=0, It should be 𝑥.𝑥=𝑥
4. 𝑥+𝑥¯=1. it is true

So option (𝐵,𝐶) are false here.

Comments

Anything OR 1 is 1 means

e.g; a+ab+cd+de+ef+1=1

a+ab=1;

x+xy+yz=1;

etc.....

Answer 3

B,C

x+1=x it is not true x+1=1 is correct

x.x=0 is not correct x.x=x is correct

 

Answer 4

B C

Answer 5

B and C is the answer