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.