Question

If B is a Boolean Algebra, then which of the following is true

(A) B is a finite but not complemented lattice.

(B) B is a finite, complemented and distributive lattice.

(C) B is a finite, distributive but not complemented lattice.

(D) B is not distributive lattic​

Answer 1

Answer:

If B is a Boolean Algebra, then which of the following is true (A) B is a finite but not complemented lattice. (B) B is a finite, complemented and distributive lattice. (C) B is a finite, distributive but not complemented lattice. (D) B is not distributive lattice

Answer 2

The Boolean Algebra B is a 'finite,' 'complemented', distributive lattice; hence, option B is correct.

• Boolean algebra includes the nullary operations, the unary operations, and the binary operations.

• Boolean algebra is a "Boolean lattice" that encapsulates the nullary operations (0,1), the complementation (the unary operations), and the binary operations.

• The characteristic feature of a Boolean lattice is that Boolean lattice is complemented and distributive.

• Boolean algebra is finite and hence forms a complete lattice.

• Thus when B is a Boolean Algebra, we can conclude by default B is 'finite,' 'complemented', and distributive lattice. Hence, option B is correct.

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