UGC NET CS 2015 Dec- paper-2
March 14, 2024Question 3714 – UGC NET CS 2015 Dec- paper-2
March 14, 2024UGC NET CS 2015 Dec- paper-2
| Question 7 |
Let P(m, n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.
(a)∃m ∀n P(m, n)
(b)∀n P(1, n)
(c) ∀m ∀n P(m, n)
(a)∃m ∀n P(m, n)
(b)∀n P(1, n)
(c) ∀m ∀n P(m, n)
| (a) – True; (b) – True; (c) – False | |
| (a) – True; (b) – False; (c) – False | |
| (a) – False; (b) – False; (c) – False | |
| (a) – True; (b) – True; (c) – True |
Question 7 Explanation:
Given P(m,n) =”m divides n”
Statement-A is ∃m ∀n P(m, n). Here, there exists some positive integer which divides every positive integer. It is true because there is positive integer 1 which divides every positive integer.
Statement-B is ∀n P(1, n). Here, 1 divided every positive integer. It is true.
Statement-C is ∀m ∀n P(m, n). Here, every positive integer divided every positive integer. It is false.
Statement-A is ∃m ∀n P(m, n). Here, there exists some positive integer which divides every positive integer. It is true because there is positive integer 1 which divides every positive integer.
Statement-B is ∀n P(1, n). Here, 1 divided every positive integer. It is true.
Statement-C is ∀m ∀n P(m, n). Here, every positive integer divided every positive integer. It is false.
Correct Answer: A
Question 7 Explanation:
Given P(m,n) =”m divides n”
Statement-A is ∃m ∀n P(m, n). Here, there exists some positive integer which divides every positive integer. It is true because there is positive integer 1 which divides every positive integer.
Statement-B is ∀n P(1, n). Here, 1 divided every positive integer. It is true.
Statement-C is ∀m ∀n P(m, n). Here, every positive integer divided every positive integer. It is false.
Statement-A is ∃m ∀n P(m, n). Here, there exists some positive integer which divides every positive integer. It is true because there is positive integer 1 which divides every positive integer.
Statement-B is ∀n P(1, n). Here, 1 divided every positive integer. It is true.
Statement-C is ∀m ∀n P(m, n). Here, every positive integer divided every positive integer. It is false.
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