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Consider the first order predicate formula φ :

Here ' a | b' denotes that „a divides b‟ where a and b are integers. Consider the following sets:
S1 {1, 2, 3, .....,100}
S2 Set of all positive integers
S3 Set of all integers
Which of the above sets satisfy φ ?
  • a)
    S1 and S3
  • b)
    S1 and S2
  • c)
    S2 and S3
  • d)
    S1, S2 and S3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the first order predicate formula φ :Here ' a | b'...
It says that for all prim number x there exist a prime number greater than x
 Where x and y are prime numbers
So for S1 = {1, 2,…..100}
For prime number 97 this is not TRUE
But S2 and S3 are infinite sets
For S2 and S3 it is always TRUE
So S2 and S3 satisfy φ.
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Consider the first order predicate formula φ :Here ' a | b' denotes that „a divides b‟ where a and b are integers. Consider the following sets:S1 {1, 2, 3, .....,100}S2 Set of all positive integersS3 Set of all integersWhich of the above sets satisfy φ ?a)S1 and S3b)S1 and S2c)S2 and S3d)S1, S2 and S3Correct answer is option 'C'. Can you explain this answer?
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