Q: Consider the following statements. A : There exists a Boolean algebra with…
2022
Q: Consider the following statements.
A : There exists a Boolean algebra with 5 elements
B : Every element of Boolean algebra has unique complement
C : If a Lattice ‘L’ is a Boolean algebra then ‘L’ is not relatively complemented
D : The direct product of two Boolean algebra is also a Boolean algebra
Choose the correct answer about the four statements given above.
- A.
Only A and D are correct
- B.
Only B and D are correct
- C.
All statement are NOT correct
- D.
All statement are correct
Attempted by 44 students.
Show answer & explanation
Correct answer: B
Statement A is false because finite Boolean algebras must have 2^n elements, and 5 is not a power of 2. Statement B is true as uniqueness of complement is a defining property. Statement C is false because Boolean algebras are relatively complemented lattices. Statement D is true as the direct product preserves Boolean algebra structure. Thus, only B and D are correct.