GATE Exam > GATE Questions > A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answe...
Start Learning for Free
A(A + B) = ?
- a)AB
- b)1
- c)(1 + AB)
- d)A
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you ...
A(A + B) = AA + AB (By Distributive Property) = A + AB (A.A = A By Commutative Property) = A(1 + B) = A*1 (1 + B = 1 by 1’s Property) = A.
Free Test
FREE
| Start Free Test |
Community Answer
A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you ...
Understanding the Expression A(A + B)
To simplify the expression A(A + B), we can utilize the properties of Boolean algebra. Let's break this down.
Step 1: Distributing A
- When we expand the expression A(A + B), we distribute A across the terms inside the parentheses:
A(A + B) = A * A + A * B
- In Boolean algebra, A * A is simply A, since any variable ANDed with itself is the variable itself.
Step 2: Simplifying the Expression
- Now, we replace A * A with A:
A(A + B) = A + A * B
- Here, A + A * B can be simplified further. According to the absorption law in Boolean algebra:
A + A * B = A
Final Result
- Therefore, the simplified result of the expression A(A + B) is A.
Conclusion
- The correct answer is option 'D' (A), as we have shown through simplification using the properties of Boolean algebra.
This reasoning confirms that the expression does not depend on B; it solely evaluates to A, making option 'D' the correct choice.
To simplify the expression A(A + B), we can utilize the properties of Boolean algebra. Let's break this down.
Step 1: Distributing A
- When we expand the expression A(A + B), we distribute A across the terms inside the parentheses:
A(A + B) = A * A + A * B
- In Boolean algebra, A * A is simply A, since any variable ANDed with itself is the variable itself.
Step 2: Simplifying the Expression
- Now, we replace A * A with A:
A(A + B) = A + A * B
- Here, A + A * B can be simplified further. According to the absorption law in Boolean algebra:
A + A * B = A
Final Result
- Therefore, the simplified result of the expression A(A + B) is A.
Conclusion
- The correct answer is option 'D' (A), as we have shown through simplification using the properties of Boolean algebra.
This reasoning confirms that the expression does not depend on B; it solely evaluates to A, making option 'D' the correct choice.
|
Explore Courses for GATE exam
|
|
Top Courses for GATEView all
Question Description
A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer?.
A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer?.
Solutions for A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A(A + B) = ?a)ABb)1c)(1 + AB)d)ACorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup