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Quantum Numbers

Consider the ...

Question

Consider the following two statement

$S_{1} : A l l c l e a r e x p l a n a t i o n s a r e s a t i s f a c t o r y,$
$S_{2} : S o m e e x c u s e s a r e u n s a t i s f a c t o r y$

Which one of the following statement follows from $S_{1} a n d S_{2}$ as per inference rules of logiv ?

Some explantions are clear excuses

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Every excuses are not clear explanations.

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Some excuses are not clear explanations

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Some excuses are clear explanations.

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Solution

The correct option is C Some excuses are not clear explanations
$S_{1} : \forall x (c l e a r (x) \to (s a t i s f a c t o r y (x))$
$S_{2} : \exists (E x c u s e (x) \land \neg s a t i s f a c t o r y (x))$
$S_{1} b y u s i n g c o n t r a p o s i t i v e r u l e$
$S_{3} : \forall x (\neg s a t i s f a c t o r y (x) \to \neg c l e a r (x))$
$B y u s i n g S_{2} a n d S_{3}$
$\exists x (e x c u s e (x) \to n o t c l e a r (i)) i . e ., s o m e e x c u s e s a r e n o t c l e a r e x p l a n a t i o n$

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Consider the following two statement S1:All clear explanations are satisfactory, S2: Some excuses are unsatisfactory Which one of the following statement follows from S1 and S2 as per inference rules of logiv ?

Consider the following two statement

$S_{1} : A l l c l e a r e x p l a n a t i o n s a r e s a t i s f a c t o r y,$
$S_{2} : S o m e e x c u s e s a r e u n s a t i s f a c t o r y$

Which one of the following statement follows from $S_{1} a n d S_{2}$ as per inference rules of logiv ?