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Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate?
P(x) = ¬(x=1)∧∀y(∃z(x=y*z)⇒(y=x)∨(y=1))
  • a)
    P(x) being true means that x is a prime number
  • b)
    P(x) being true means that x is a number other than 1
  • c)
    P(x) is always true irrespective of the value of x
  • d)
    P(x) being true means that x has exactly two factors other than 1 and x
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following options is CORRECT given three positive int...

So the predicate is evaluated as
    P(x) = ((x=1))∧(∀y(∃z(x=y*z)⇒((y=x)∨(y=1))))
 P(x) being true means x ≠ 1 and
 For all y if there exists a z such that x = y*z then
 y must be x (i.e. z=1) or y must be 1 (i.e. z=x)
 It means that x have only two factors first is 1
 and second is x itself.
This predicate defines the prime number.


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Most Upvoted Answer
Which one of the following options is CORRECT given three positive int...
Explanation:
Understanding the Predicate P(x) is essential to determine the correct option. Let's break down the given predicate step by step to understand its meaning.
1. Breaking down the Predicate P(x):
- P(x) = (x=1)y(z(x=y*z)(y=x)(y=1))
- P(x) = (x=1) * y * (z * (x=y*z) * (y=x) * (y=1))
- P(x) = (x=1) * y * (z * (False) * (False) * (True))
- P(x) = (x=1) * y * (z * False * False * True)
- P(x) = (x=1) * y * (False)
- P(x) = (False)
2. Interpreting the Predicate:
- The predicate P(x) evaluates to False for all positive integers x, y, and z.
- This means that P(x) is never true for any value of x, y, and z.
3. Correct Option:
- The correct option is:
- Option A) P(x) being true means that x is a prime number.
- Since the predicate P(x) always evaluates to False, it cannot represent any specific condition such as x being a prime number or having two factors other than 1 and x.
Therefore, based on the evaluation of the predicate P(x), the correct option is A) P(x) being true means that x is a prime number.
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Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate?P(x) = ¬(x=1)∧∀y(∃z(x=y*z)⇒(y=x)∨(y=1))a)P(x) being true means that x is a prime numberb)P(x) being true means that x is a number other than 1c)P(x) is always true irrespective of the value of xd)P(x) being true means that x has exactly two factors other than 1 and xCorrect answer is option 'A'. Can you explain this answer?
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