Post Closed as "off-topic" by Joseph Weissman
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Every dog and cat who is well trained is a good pet.

(F: a is a dog; G: a is a cat; H: a is well trained; I: a is a good pet.)

Here are my options:

a) ∀x((Fx∨Gx)∧Ix→Hx)

b) ∀x((Fx∨Gx)∧Hx→Ix)

c) ∀x((Fx∧Gx)∧Hx→Ix)

d) ∀x∀y(Fx∧Gy∧Hx→Ix)

For a) I interpret it as: for all dogs or cats and if the dog or cat is well trained, then the dog or cat is a good pet. Makes sense...

for b) I interpret it as: for all dogs or cats and if it's a good pet, then it is well trained. I don't think this one is right since it means that being a good pet implies well trained but the statement says: well trained implies good pet

for c) for all things that are dogs and cats and is well trained it implies good pet. (i don't think it's this one because you cant be a dog and a cat)

for d) I'm not sure about this one? I heardread that the ordering of the quantifiers matter but I'm not too sure. Also the it only applies for either a dog or a cat since it is Hx -> lx and not Hy -> Ly. can someone help me with this one?

i think it's a)... need guidance thank you.

Every dog and cat who is well trained is a good pet.

(F: a is a dog; G: a is a cat; H: a is well trained; I: a is a good pet.)

Here are my options:

a) ∀x((Fx∨Gx)∧Ix→Hx)

b) ∀x((Fx∨Gx)∧Hx→Ix)

c) ∀x((Fx∧Gx)∧Hx→Ix)

d) ∀x∀y(Fx∧Gy∧Hx→Ix)

For a) I interpret it as: for all dogs or cats and if the dog or cat is well trained, then the dog or cat is a good pet. Makes sense...

for b) I interpret it as: for all dogs or cats and if it's a good pet, then it is well trained. I don't think this one is right since it means that being a good pet implies well trained but the statement says: well trained implies good pet

for c) for all things that are dogs and cats and is well trained it implies good pet. (i don't think it's this one because you cant be a dog and a cat)

for d) I'm not sure about this one? I heard that the ordering of the quantifiers matter but I'm not too sure. Also the it only applies for either a dog or a cat since it is Hx -> lx and not Hy -> Ly. can someone help me with this one?

i think it's a)... need guidance thank you.

Every dog and cat who is well trained is a good pet.

(F: a is a dog; G: a is a cat; H: a is well trained; I: a is a good pet.)

Here are my options:

a) ∀x((Fx∨Gx)∧Ix→Hx)

b) ∀x((Fx∨Gx)∧Hx→Ix)

c) ∀x((Fx∧Gx)∧Hx→Ix)

d) ∀x∀y(Fx∧Gy∧Hx→Ix)

For a) I interpret it as: for all dogs or cats and if the dog or cat is well trained, then the dog or cat is a good pet. Makes sense...

for b) I interpret it as: for all dogs or cats and if it's a good pet, then it is well trained. I don't think this one is right since it means that being a good pet implies well trained but the statement says: well trained implies good pet

for c) for all things that are dogs and cats and is well trained it implies good pet. (i don't think it's this one because you cant be a dog and a cat)

for d) I'm not sure about this one? I read that the ordering of the quantifiers matter but I'm not too sure. Also the it only applies for either a dog or a cat since it is Hx -> lx and not Hy -> Ly. can someone help me with this one?

i think it's a)... need guidance thank you.

1

# need some guidance for this easy symbolic logic question

Every dog and cat who is well trained is a good pet.

(F: a is a dog; G: a is a cat; H: a is well trained; I: a is a good pet.)

Here are my options:

a) ∀x((Fx∨Gx)∧Ix→Hx)

b) ∀x((Fx∨Gx)∧Hx→Ix)

c) ∀x((Fx∧Gx)∧Hx→Ix)

d) ∀x∀y(Fx∧Gy∧Hx→Ix)

For a) I interpret it as: for all dogs or cats and if the dog or cat is well trained, then the dog or cat is a good pet. Makes sense...

for b) I interpret it as: for all dogs or cats and if it's a good pet, then it is well trained. I don't think this one is right since it means that being a good pet implies well trained but the statement says: well trained implies good pet

for c) for all things that are dogs and cats and is well trained it implies good pet. (i don't think it's this one because you cant be a dog and a cat)

for d) I'm not sure about this one? I heard that the ordering of the quantifiers matter but I'm not too sure. Also the it only applies for either a dog or a cat since it is Hx -> lx and not Hy -> Ly. can someone help me with this one?

i think it's a)... need guidance thank you.