UGC NET 2018 :
Consider a vocabulary with only four propositions A, B, C and D. How many models are there for the following sentence ?
A) 10
B) 12
C) 15
D) 16
Solution:
We know there are total 24 = 16 cases.
S.No | A | B | C | D | B v C |
1 | 0 | 0 | 0 | 0 | 0 |
2 | 0 | 0 | 0 | 1 | 0 |
3 | 0 | 0 | 1 | 0 | 1 |
4 | 0 | 0 | 1 | 1 | 1 |
5 | 0 | 1 | 0 | 0 | 1 |
6 | 0 | 1 | 0 | 1 | 1 |
7 | 0 | 1 | 1 | 0 | 1 |
8 | 0 | 1 | 1 | 1 | 1 |
9 | 1 | 0 | 0 | 0 | 0 |
10 | 1 | 0 | 0 | 1 | 0 |
11 | 1 | 0 | 1 | 0 | 1 |
12 | 1 | 0 | 1 | 1 | 1 |
13 | 1 | 1 | 0 | 0 | 1 |
14 | 1 | 1 | 0 | 1 | 1 |
15 | 1 | 1 | 1 | 0 | 1 |
16 | 1 | 1 | 1 | 1 | 1 |
From the table above, B V C is false. If B = C = 0.
There is 4 time B V C = 0.
So, 16 – 4 = 12 Ans.