IGNOU MCS 13 2012 - What is Boolean algebra? Explain how Boolean algebra methods are used

Question

What is Boolean algebra? Explain how Boolean algebra methods are used in logic circuit design.

02 Nov 2017

Answer :

Word Count : 1122

Definition: A Boolean algebra B is an algebraic structure which consists of a set X (≠ Ø) having

two binary operations (denoted by ∨ and ∧), one unary operation (denoted by ' ) and two specially

defined elements O and I (say), which satisfy the following five laws for all x, y, z ∈ X.

B1. Associative Laws: x ∨ (y ∨ z) = (x ∨ y) ∨ z,

x ∧ (y ∧ z) = (x ∧ y) ∧ z

B2. Commutative Laws: x ∨ y = y ∨ x,

x ∧ y = y ∧ x

B3. Distributive Laws: x ∨ (y ∧ z) = (x ∨ y) ∧ (x ∨ z),

x ∧ (y ∨ z) = (x ∧ y) ∨ (x ∧ z)

B4. Identity Laws: x ∨ O = x,

x ∧ I = x

B5. Complementation

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