Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Let # be a binary operator defined as X # Y =...
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Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.
S1: (P # Q) # R = P # (Q # R)
S2: Q # R = R # Q
Which of the following is/are true for the Boolean variables P, Q and R?
- a)Only S1 is True
- b)Both S1 and S2 are True
- c)Only S2 is True
- d)Neither S1 nor S2 are True
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Let # be a binary operator defined as X # Y = X′ + Y′ wher...
S2 is true, as X' + Y' = Y' + X'
S1 is false.
Let P = 1, Q = 1, R = 0, we get different results
(P # Q) # R = (P' + Q')' + R' = (0 + 0)' + 1 = 1 + 1 = 1
P # (Q # R) = P' + (Q' + R')' = 0 + (0 + 1)' = 0 + 0 = 0
Let P = 1, Q = 1, R = 0, we get different results
(P # Q) # R = (P' + Q')' + R' = (0 + 0)' + 1 = 1 + 1 = 1
P # (Q # R) = P' + (Q' + R')' = 0 + (0 + 1)' = 0 + 0 = 0
Most Upvoted Answer
Let # be a binary operator defined as X # Y = X′ + Y′ wher...
Understanding the Operator #
The binary operator # is defined as follows for Boolean variables X and Y:
- **X # Y = X' + Y'**
Here, X' and Y' represent the complements of X and Y respectively. The operator essentially computes the logical OR of the complements of two Boolean variables.
Analyzing Statement S1
**Statement:** (P # Q) # R = P # (Q # R)
Let's simplify both sides:
- **Left Side:**
(P # Q) # R = (P' + Q') # R
= (P' + Q')' + R'
= P''Q'' + R'
= PQ + R'
- **Right Side:**
P # (Q # R) = P # (Q' + R')
= P' + (Q' + R')'
= P' + QR
Thus,
- Left Side: PQ + R'
- Right Side: P' + QR
Since PQ + R' ≠ P' + QR in general, S1 is **False**.
Analyzing Statement S2
**Statement:** Q # R = R # Q
Using the operator definition:
- **Left Side:**
Q # R = Q' + R'
- **Right Side:**
R # Q = R' + Q'
Both sides yield the same expression, confirming that S2 is **True**.
Conclusion
- **S1 is False**
- **S2 is True**
Therefore, the correct option is **C) Only S2 is True**.
The binary operator # is defined as follows for Boolean variables X and Y:
- **X # Y = X' + Y'**
Here, X' and Y' represent the complements of X and Y respectively. The operator essentially computes the logical OR of the complements of two Boolean variables.
Analyzing Statement S1
**Statement:** (P # Q) # R = P # (Q # R)
Let's simplify both sides:
- **Left Side:**
(P # Q) # R = (P' + Q') # R
= (P' + Q')' + R'
= P''Q'' + R'
= PQ + R'
- **Right Side:**
P # (Q # R) = P # (Q' + R')
= P' + (Q' + R')'
= P' + QR
Thus,
- Left Side: PQ + R'
- Right Side: P' + QR
Since PQ + R' ≠ P' + QR in general, S1 is **False**.
Analyzing Statement S2
**Statement:** Q # R = R # Q
Using the operator definition:
- **Left Side:**
Q # R = Q' + R'
- **Right Side:**
R # Q = R' + Q'
Both sides yield the same expression, confirming that S2 is **True**.
Conclusion
- **S1 is False**
- **S2 is True**
Therefore, the correct option is **C) Only S2 is True**.
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Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.S1: (P # Q) # R = P # (Q # R)S2: Q # R = R # QWhich of the following is/are true for the Boolean variables P, Q and R?a)Only S1 is Trueb)Both S1 and S2 are Truec)Only S2 is Trued)Neither S1 nor S2 are TrueCorrect answer is option 'C'. Can you explain this answer?
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Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.S1: (P # Q) # R = P # (Q # R)S2: Q # R = R # QWhich of the following is/are true for the Boolean variables P, Q and R?a)Only S1 is Trueb)Both S1 and S2 are Truec)Only S2 is Trued)Neither S1 nor S2 are TrueCorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.S1: (P # Q) # R = P # (Q # R)S2: Q # R = R # QWhich of the following is/are true for the Boolean variables P, Q and R?a)Only S1 is Trueb)Both S1 and S2 are Truec)Only S2 is Trued)Neither S1 nor S2 are TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let # be a binary operator defined as X # Y = X′ + Y′ where X and Y are Boolean variables. Consider the following two statements.S1: (P # Q) # R = P # (Q # R)S2: Q # R = R # QWhich of the following is/are true for the Boolean variables P, Q and R?a)Only S1 is Trueb)Both S1 and S2 are Truec)Only S2 is Trued)Neither S1 nor S2 are TrueCorrect answer is option 'C'. Can you explain this answer?.
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