Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which Of the following statements are true?S1...
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Which Of the following statements are true?
S1: Every Distributive lattice has unique complement.
S2: In Complemented lattice every element has at least one complement.
S3: Boolean lattice is both complemented and distributive.
S4: In Boolean lattice every lattice has exactly one complement.
S1: Every Distributive lattice has unique complement.
S2: In Complemented lattice every element has at least one complement.
S3: Boolean lattice is both complemented and distributive.
S4: In Boolean lattice every lattice has exactly one complement.
- a)S1 & S4
- b)S1, S2 & S3
- c)S2, S3 & S4
- d)All of these statements
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which Of the following statements are true?S1:Every Distributive latti...
Clearly S1 is wrong because in distributive lattice a element may have zero complement. Rest other statements are properties of the corresponding lattices.
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Which Of the following statements are true?S1:Every Distributive latti...
Understanding Distributive and Complemented Lattices
To analyze the statements regarding lattices, let's clarify some concepts.
1. Distributive Lattice and Unique Complements (S1)
- A distributive lattice does not require every element to have a unique complement. Therefore, S1 is false.
2. Complemented Lattice (S2)
- In a complemented lattice, every element indeed has at least one complement. Thus, S2 is true.
3. Boolean Lattice (S3)
- A Boolean lattice is a specific type of complemented lattice that is also distributive. Hence, S3 is true.
4. Complements in Boolean Lattice (S4)
- In a Boolean lattice, every element has a unique complement. Thus, S4 is true.
Conclusion
- Based on the evaluations:
- S1: False
- S2: True
- S3: True
- S4: True
Hence, the only true statements are S2, S3, and S4, making the correct option C.
To analyze the statements regarding lattices, let's clarify some concepts.
1. Distributive Lattice and Unique Complements (S1)
- A distributive lattice does not require every element to have a unique complement. Therefore, S1 is false.
2. Complemented Lattice (S2)
- In a complemented lattice, every element indeed has at least one complement. Thus, S2 is true.
3. Boolean Lattice (S3)
- A Boolean lattice is a specific type of complemented lattice that is also distributive. Hence, S3 is true.
4. Complements in Boolean Lattice (S4)
- In a Boolean lattice, every element has a unique complement. Thus, S4 is true.
Conclusion
- Based on the evaluations:
- S1: False
- S2: True
- S3: True
- S4: True
Hence, the only true statements are S2, S3, and S4, making the correct option C.
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Which Of the following statements are true?S1:Every Distributive lattice has unique complement.S2:In Complemented lattice every element has at least one complement.S3:Boolean lattice is both complemented and distributive.S4:In Boolean lattice every lattice has exactly one complement.a)S1 & S4b)S1, S2 & S3c)S2, S3 & S4d)All of these statementsCorrect answer is option 'C'. Can you explain this answer?
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