UGC NET 2018 :
Consider the vocabulary with only four propositions A,B,C and D. How many models are there for the following sentence ?
A) 8
B) 7
C) 15
D) 16
Solution:
We know there are total 24 = 16 cases.
As shown in below truth table, it won’t satisfy the condition when A = B = C = D = 0.
|
S.No |
A |
B |
C |
D |
(⌐ A ∨ ⌐B ∨ ⌐C ∨ ⌐ D) |
|
1 |
0 |
0 |
0 |
0 |
0 |
|
2 |
0 |
0 |
0 |
1 |
1 |
|
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 |
1 |
|
10 |
1 |
0 |
0 |
1 |
1 |
|
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 |
So, from the given sentence false(0) occurs only if A, B, C and D are false(0) which occurs 1 time.
Required number of models = 16 – 1 = 15.