LIST-I (Name) LIST-II (Identity) A. Domination law I. $x + 1 = 1$ B. Associative law II. $x + (yz) = (x + y)(x + z)$ C. Distributive law III. $x + xy = x$ D. Absorption law IV. $x + (y + z) = (x + y) + z$
Boolean Identities Matching Solution
This solution details the matching process for standard Boolean algebra identities provided in LIST-I and LIST-II.
Identifying Boolean Identities
- A. Domination law: This law relates to how a variable interacts with constants 0 or 1 using OR or AND operations. For the OR operation, the identity is $x + 1 = 1$. This matches LIST-II I.
- B. Associative law: This law deals with the grouping of operands in operations. For the OR operation, it is $x + (y + z) = (x + y) + z$. This matches LIST-II IV.
- C. Distributive law: This law describes how one operation is distributed over another. The identity $x + (yz) = (x + y)(x + z)$ shows the distribution of OR over AND. This matches LIST-II II.
- D. Absorption law: This law simplifies expressions involving AND and OR operations. The identity $x + xy = x$ is a key example. This matches LIST-II III.
Consolidated Matches
Based on the analysis of each law:
A (Domination law) matches with I ($x + 1 = 1$).
B (Associative law) matches with IV ($x + (y + z) = (x + y) + z$).
C (Distributive law) matches with II ($x + (yz) = (x + y)(x + z)$).
D (Absorption law) matches with III ($x + xy = x$).
The correct pairing is therefore A-I, B-IV, C-II, D-III.
Important Questions from Boolean Algebra
How many different Boolean functions of degree n are there?
Consider a Boolean function of ‘n’ variables. The order of an algorithm that determines whether the Boolean function produces a output 1 is:
The marginal probability of cavity P(cavity) is ________.
The probability of a cavity, given evidence of a toothache, P(cavity | toothache) is _________.
The probability of a toothache, given evidence of a cavity, P(toothache | cavity) is ________.
