GATE CSE 2014 Set 3 | Question: 53

Question

The CORRECT formula for the sentence, "not all Rainy days are Cold" is

• A. $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$
• B. $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$
• C. $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$
• D. $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$

Comments

Can I write logic for "All rainy days are cold." and then do the negation. Will that be correct?

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Yes. That will be correct.

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Thanks!

Answer 1

"Not all Rainy days are Cold" are also rewrite “There exists at least one  Rainy day are  not Cold”    

Answer 2

"not all Rainy days are Cold" 

~∀d (Rainy(d)    —>  Cold(d))

~∀d (~Rainy(d)  +  Cold(d))               

 ∃d (Rainy(d)  ^  ~ Cold(d))                Some rainy days are not cold.

 

i hope my answer helps u a lot.

Answer 3

Not all rainy days are cold which is

$\neg(\forall d(\text{Rainy}(d)\rightarrow \text{Cold}(d) ))$

$\neg(\forall d(\neg\text{Rainy}(d) \lor \text{Cold}(d) ))$

$(\exists \neg d(\neg\text{Rainy}(d) \lor \text{Cold}(d) ))$

$(\exists d(\text{Rainy}(d) \land \neg\text{Cold}(d) ))$

Option $D$

Comments

we get to conclusion

1.some rainy day are cold

or

2.some rainy day are not cold

 

so according to option d we get sme rainy day are not cold ..

so may be it is correct method .

if i am in correct then please correct me