UGC NET CS 2018 July - II Question 75

Question 75

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

Options:

1. (1) 10
2. (2) 12
3. (3) 15
4. (4) 16

Answer : (2) 12

Explanation Question 75

We know there are total 2⁴ = 16 cases.
As shown in below truth table, it won't satisfy the condition when B = C = 0.

A	B	C	D	B v C
0	0	0	0	0
0	0	0	1	0
0	0	1	0	1
0	0	1	1	1
0	1	0	0	1
0	1	0	1	1
0	1	1	0	1
0	1	1	1	1
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	1
1	1	0	0	1
1	1	0	1	1
1	1	1	0	1
1	1	1	1	1

So, from the given sentence false(0) occurs only if B and C are false(0) which occurs 4 times.
Required number of models = 16 - 4 = 12.

Hence, Option (2) is correct answer.

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