The following arguments are all valid. Turn in informal proofs of their validity

Question

The following arguments are all valid. Turn in informal proofs of their validity. You may find it helpful to translate the arguments into FOL before trying to give proofs, though that's not required. Explicitly note any inferences using modus ponens, biconditional elimination, or conditional proof. The unicorn, if it is not mythical, is a mammal, but if it is mythical, it is immortal. If the unicorn is either immortal or a mammal, it is horned. The unicorn, if horned, is magical. The unicorn is magical. The unicorn, if horned, is elusive and magical, but if not horned, it is neither. If the unicorn is not horned, it is not mythical. The unicorn is horned if and only if magical or mythical. The unicorn, if homed, is elusive and dangerous. If elusive or mythical, the unicorn is rare. If a mammal, the unicorn is not rare. The unicorn, if horned, is not a mammal. a is a large tetrahedron or a small cube. b is not small. If a is a tetrahedron or a cube, then b is large or small. a is a tetrahedron only if b is medium. a is small and b is large.

Explanation / Answer

Let

p - unicorn mythical

q - unicorn mammal

r - mortal

s - horned

t - magical

Given that ~p --> q, p-->~r, qv~r --> s, s--> t, t is true.

Since unicorn is magical, unicorn is horned.

Since it is horned it is either immortal or a mammal.

If immortal, unicorn is mammal and if it is mammal it is not mythical

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