Match the columns.

Match the LIST – I with LIST – II.

	​List – I ​(Boolean Algebra Law)​		​List – II (Axioms)​
A.	Absorption Law	I.	​$$a+1=1$$​​
B.	Bounded Law	II.	​$$a+0=a$$​​
C.	Identity Law	III.	​$$a^{*}(b+c)=(a^{*}b)+(a^{*}c)$$​​
D.	Distributive Law	IV.	​$$a+(a^{*}b)=a$$​​

Choose the correct answer from the options given below:

Correct option is A

We are asked to match the Boolean Algebra Laws with their corresponding axioms.
A. Absorption Law:
• The Absorption Law in Boolean algebra states:
​$$a + (a \cdot b) = a$$​​
• This matches with IV. $$\bf{a + (a \cdot b) = a}$$​, which is the axiom corresponding to the Absorption Law.
B. Bounded Law:
• The Bounded Law in Boolean algebra states:
​$$a + 0 = a \quad \text{and} \quad a \cdot 1 = a$$​​
• This matches with I. a + 0 = a, which is the axiom corresponding to the Bounded Law.
C. Identity Law:
• The Identity Law in Boolean algebra states:
​$$a + 1 = 1 \quad \text{and} \quad a \cdot 0 = 0$$​​
• This matches with II. a + 1 = 1, which is the axiom corresponding to the Identity Law.
D. Distributive Law:
• The Distributive Law in Boolean algebra states:
​$$a \cdot (b + c) = (a \cdot b) + (a \cdot c)$$​​
• This matches with III. $$\bf{a \cdot (b + c) = (a \cdot b) + (a \cdot c)}$$​, which is the axiom corresponding to the Distributive Law.
Information Booster:
1. Absorption Law allows simplification of Boolean expressions by eliminating redundant terms.
2. Bounded Law establishes the identity elements for the operations of addition (0) and multiplication (1).
3. Identity Law ensures that certain operations (adding 1 or multiplying by 0) have a consistent result.
4. Distributive Law allows us to "distribute" one operation over another, making it easier to simplify complex Boolean expressions.