Predicate Logic - Some Days are not Rainy

91 Views Asked by At

The following statement needs to be converted into Predicate logic.

Some days are not rainy.

Universe is everything in this world.

Our faculty gave the following answer ->

$\lnot (\forall x D(x) \land R(x)) $

Where, D(x) means x is a day And R(x) means x is rainy.

I am somewhat confused with the following answer. I believe it does not match with the statement above.

1

There are 1 best solutions below

1
On BEST ANSWER

The "literal" translation would be $$\exists x\ (D(x)\wedge \neg R(x))\ .$$ This is equivalent to $$\neg\forall x\ (\neg D(x)\vee R(x))$$ or $$\neg\forall x\ (D(x)\to R(x))\ ,$$ but not to the answer they gave.