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

$B \vee C$

  1. 10
  2. 12
  3. 15
  4. 16
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3 Answers

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A

B

C

D

BVC

F

F

F

F

F

F

F

F

T

F

F

F

T

F

T

F

F

T

T

T

F

T

F

F

T

F

T

F

T

T

F

T

T

F

T

F

T

T

T

T

T

F

F

F

F

T

F

F

T

F

T

F

T

F

T

T

F

T

T

T

T

T

F

F

T

T

T

F

T

T

T

T

T

F

T

T

T

T

T

T

So from the given sentence false(F) occurs only if B and C are false(F) which occurs 4 times. so 16-4=12.

hence option B is the ans.

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Answer B

We know there are total 2^4 = 16 cases.

It won't satisfy the condition when B = C = 0. A and D can choose their elements in 2C1 ways (0 or 1).

Thus, there 2C1 * 2C1 = 4 cases that violates the condition

Required number of models = 16 - 4 = 12

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