Aspire Faculty ID #17438 · Topic: UGC NET Computer Science June 2024 (Paper II) · Just now
UGC NET Computer Science June 2024 (Paper II)

Which of the following have truth values if universe of discourse consists of all integers?

A. $\forall n \exists m (n^2 < m)$
B. $\exists m \forall n (n < m^2)$
C. $\exists n \exists m (n^2 + m^2 = 5)$
D. $\exists n \exists m (n^2 + m^2 = 6)$
E. $\exists n \exists m (n+m=4 \land n-m=1)$

Choose the correct answer from the options given below :

Solution

A:

For every integer $n$, choose $m=n^2+1$

Then $n^2<m$ → True


B:

$\exists m$ such that $n<m^2$ for all integers $n$.

But integers are unbounded → False


C:

$n^2+m^2=5$


Example: $1^2+2^2=5$ → True


D:

$n^2+m^2=6$


No integer solution → False


E:

$n+m=4$

$n-m=1$


Add equations:


$2n=5$ → $n=2.5$ (not integer) → False


True statements: A and C

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