Question:
In case of three attributes A, B and C, the class frequency \((\alpha B \gamma)\) (that is, B present, A and C absent) in terms of other class frequencies is:
In case of three attributes A, B and C, the class frequency \((\alpha B \gamma)\) (that is, B present, A and C absent) in terms of other class frequencies is:
Show Hint
Split the population by presence/absence of A, B, C into eight parts and check which formula isolates exactly one non-negative part.
Updated On: Jul 4, 2026
- \((AB) + (AC) - (B) - (ABC)\)
- \((ABC) - (B) + (AB) - (BC)\)
- \((ABC) - (A) - (C) + (B)\)
- \((B) - (AB) - (BC) + (ABC)\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: In the notation of attributes, capital letters A, B, C denote presence, and the corresponding Greek letters denote absence. So \((\alpha B\gamma)\) is the class having B present but A and C absent.
Step 2: By inclusion-exclusion, \((B)\) (units with B present, regardless of A and C) must be reduced by the units that also carry A, i.e. \((AB)\), and by units that also carry C, i.e. \((BC)\). Units carrying B, A and C together, i.e. \((ABC)\), get removed twice in this process, so they are added back once.
Step 3: This gives the identity \[(\alpha B \gamma) = (B) - (AB) - (BC) + (ABC)\]
Step 4: This matches option (D) exactly.
\[\boxed{(\alpha B\gamma) = (B) - (AB) - (BC) + (ABC)}\]Was this answer helpful?
0
0
Top CPET Statistics Questions
- The statements below relate to Bayes theorem in probability:
(i) Bayes theorem gives a formula to compute conditional probability.
(ii) The posterior probability computed by Bayes theorem supersedes the prior probability.
(iii) Bayes theorem can be used to compute probabilities of past events on the basis of the occurrences of subsequent events.
Identify the correct answer: - If \(P(A) = 0.25\), \(P(B|A) = 0.5\), \(P(B|\bar{A}) = 0.75\) then \(P(A|B)\) is ______.
- Three functions \(F_1(x)\), \(F_2(x)\) and \(F_3(x)\) are defined below:
(i) \(F_1(x) = 0\), for all \(x \in (-\infty, +\infty)\)
(ii) \(F_2(x) = 1\), for all \(x \in (-\infty, +\infty)\)
(iii) \(F_3(x) = 0\), for all \(x \le 0\) and \(F_3(x) = 1\), for all \(x > 0\)
Which of the above functions is a distribution function of a random variable? - If a random variable \(X\) has mean 3 and standard deviation 5, then the variance of \(Y = 2X - 5\) is:
- Three numbers \(X\), \(Y\), \(Z\) are randomly drawn from the set \(\{1, 2, 3, 4\}\). \(E(XYZ)\) is equal to:
View More Questions
Top CPET Theory of Attributes Questions
Top CPET Questions
- Which of the following is a key reason for choosing DRAM over SRAM for main memory?
- Which of the following components in an FPGA is responsible for implementing combinational and sequential logic?
- What is the main purpose of declaring a base class as virtual in multiple inheritance?
- What happens if a class contains at least one pure virtual function?
- What happens if a derived class defines a function with the same name as a base class function, but with a different parameter list?
View More Questions