Using predicate symbols shown below and appropriate quantifiers, write each English language statement as a predicate wff.
Domain is all the objects in world.
- B(x) : x is a bee
- F(x) : x is a flower
- L(x,y) : x loves y
Following are the statements along with my attempt at the question.
Kindly give a hint if any ( or all 🙁 ) of the following are wrong.
An English translation of my attempted solution would be very helpful in case I did it wrong.
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All Bees love all flowers
$\forall$ b $\forall$ f ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
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Some Bees love all flowers
$\forall$ f $\exists$ b ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
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All Bees love some flowers
$\forall$ b ( B(b) $\wedge$ ( $\exists$ f ( F(f) $\rightarrow$ L(b,f) )
or this
$\forall$ b $\exists$ f ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
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Every bee hates only flowers.
(This 'only' is particularly causing confusion, should I account for the fact that there are other non-flower objects in domain )
$\forall$ b $\forall$ f ( B(b) $\wedge$ F(f) $\rightarrow$ $\neg$ L(b,f) )
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Every bee hates all flowers
$\forall$ b $\forall$ f ( B(b) $\wedge$ F(f) $\rightarrow$ $\neg$ L(b,f) )
Best Answer
All Bees love all flowers
$\forall$ b $\forall$ f ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
Some Bees love all flowers
$\forall$ f $\exists$ b ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
All Bees love some flowers
$\forall$ b ( B(b) $\wedge$ ( $\exists$ f ( F(f) $\rightarrow$ L(b,f) )
or this
$\forall$ b $\exists$ f ( B(b) $\wedge$ F(f) $\rightarrow$ L(b,f) )
Every bee hates only flowers.
(This 'only' is particularly causing confusion, should I account for the fact that there are other non-flower objects in domain ).
Every bee hates all flowers
$\forall$ b $\forall$ f ( B(b) $\wedge$ F(f) $\rightarrow$ $\neg$ L(b,f) )