Only four propositions, How many models for B v C | UGC NET

UGC NET 2018 : 

Consider a vocabulary with only four propositions A, B, C and D. How many models are there for the following sentence ?

B v C

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.