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correct formula for not all sunny days are hot

1 vote
176 views


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in Mathematical Logic 176 views

1 Answer

1 vote
 
Best answer

Sunny(x)= x is a sunny day

Hot(x)=x is a hot day

All Sunny Days are hot:-

∀x (Sunny(x)->Hot(x))

Not All Sunny days are hot=Not(All sunny days are hot)

Not(∀x (Sunny(x)  -> Hot(x)))

Not(∀x (~Sunny(x) V Hot(x) ) )

(∃ x ~(~Sunny(x) V Hot(x) ) )

∃ X(Sunny(x) AND ~Hot(x))

So,  option D is the answer


selected by
1
"Not all sunny days are hot" can be interpreted as

"There exist some sunny days that are not hot".

$\Rightarrow$ $\exists$ d (Sunny(d) ^ ~hot(d)).
0
Negating the statement "All sunny days are hot"

we will get Not all sunny days are hot it will give option D.
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