Question

Is this logic valid? All diamonds shine. This mineral shines. Therefore this mineral is a diamond.

Answer 1

The conclusion does not logically follow from the premises.

Explanation:

The first premise is that "All diamonds shine."

But that does not mean that ONLY diamonds shine.
Lots of things also shine besides diamonds.

Aluminum foil shines, and plastic, and glass.
Emeralds and rubies shine too, but they are not diamonds.
The moon, and flashlights, and light bulbs shine too.

The first premise, "All diamonds shine", really means
`"All diamonds shine, but so do many other things."`

IF the first premise said
"ONLY diamonds shine," then it would be logical to say that Mineral X has to be a diamond because it shines

That conclusion would be `lo` `gical` but `i` `nc` `o` `r` `rect` because the premise is incorrect.
Diamonds are actually not the ONLY things that shine.

Answer 2

`D->S`
`X->S`
`X->D` is False.

Explanation:

Let's do this with symbols.

We can set `D="All diamonds"` and `S="shine"`

We're told that all diamonds shine. And so if it's a diamond, it shines:

`D->S`

Let's now set `X="mineral X"`. We're told mineral X shines, and if it's mineral X, it shines:

`X->S`

Note that the arrows only go one way - we really don't know anything about `S` aside from the fact that `D` and `X` are a part of `S`. And `X` and `D` are two totally different things. We're not told anything about the relationship between `X` and `D`. And so the contention that

`X->D` is False.

Answer 3

Counterexample to anyone claiming that this reasoning is valid.

Explanation:

All dogs have fur.
This has fur.

But this is not a dog, it is a cat.