Consider the following statements:
A. There exists a Boolean algebra with 5 elements.
B. Every element of a Boolean algebra has a unique complement.
C. If a lattice L is a Boolean algebra then L is not relatively complemented.
D. The direct product of two Boolean algebras is also a Boolean algebra.
Choose the correct answer about the four statements.
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: B. Only B and D are correct
Explanation
A finite Boolean algebra has 2n elements, so A is false. B is true (distributive and complemented). A Boolean algebra is relatively complemented, so C is false. D is true.More Discrete Structures and Optimisation questions
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