Consider a vocabulary with only four propositions A, B, C and D.
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Consider a vocabulary with only four propositions A, B, C and D. How many models are there for the following sentence?
B ∨ CA. 10
B. 12
C. 15
D. 16
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concepts:
Number of models is nothing but number of TRUE in final statement.
Sentence.: B ∨ C
Truth Table:
|
A |
B |
C |
D |
B ∨ C |
|
T |
T |
T |
T |
T |
|
T |
T |
T |
F |
T |
|
T |
T |
F |
T |
T |
|
T |
T |
F |
F |
T |
|
T |
F |
T |
T |
T |
|
T |
F |
T |
F |
T |
|
T |
F |
F |
T |
F |
|
T |
F |
F |
F |
F |
|
F |
T |
T |
T |
T |
|
F |
T |
T |
F |
T |
|
F |
T |
F |
T |
T |
|
F |
T |
F |
F |
T |
|
F |
F |
T |
T |
T |
|
F |
F |
T |
F |
T |
|
F |
F |
F |
T |
F |
|
F |
F |
F |
F |
F |
12 models are there for given Sentence.
Tips and Tricks:
Number of variables = 4
Statement possible = 24 = 16
Since (B ∨ C) OR operation between two variables ∴ ¾ of total cases will be true.
Therefore, number of modes = ¾ × 16 = 12