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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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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