Your argument in propositional logic:

An invalid argument, is an argument whose conclusion is false even if the premises are true. We normally try to invalidate an argument, if we fail then it is valid.

Let us set the premises to true (1), and the conclusion to false (0), and see if this is possible.

- S v R = 1
- ~S & ~R = 1
- ∴ B = 0

For the conclusion to be false, B has to be false, so we put 0 next to B.

- S v R = 1
- ~S & ~R = 1
- ∴ B0 = 0

For `~S & ~R`

to be true, both R and S have to be false, so we put 0 next to R and S in the whole argument.

- S0 v R0 = 1
**(but this cannot be 1)**
- ~S0 & ~R0 = 1
- ∴ B0 = 0

As you can see, the first premise cannot be true since 0 v 0 = 0 not 1.

As you can see, we could not set the premises to 1 and the conclusion to 0, so **the argument is valid**.

This is how I check if propositional arguments are valid, first I set the conclusion to false (0), and the premises to 1, and I work my way through the premises to check if this is possible, if it is not possible, then the argument has to be valid.

**Notes**

The reason why the argument's conclusion does not make sense is because it violates the law of non-contradiction. So, there is an inconsistency in the premises.

**So, why does this inconsistency make the argument valid?**

Simply because, it is impossible for two inconsistent premises (two premises that are contradictory) to be both true. That is why it is **intrinsically** impossible for all the premises to be true.

Which makes it **intrinsically** impossible for the conclusion to be false and the premises to be true (Hence it is impossible to invalidate the argument), this is the reason the result (by formal standards) is a valid argument.

And although the argument is formally valid (according to our definition of validity), it is fallacious, and therefore can be considered, informally at least, a bad argument, and there is a good reason to reject such an argument.

Additionally, the argument commits a black and white (false dilemma) fallacy, the first premise `either it is sunny or raining`

to be specific. It can be neither sunny or raining i.e : Cloudy day`. This false dilemma is what makes the premises sound true (to some) in a natural human language.

https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/112/Inconsistency

https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/94/False-Dilemma

Neither term in the conclusion appears in the premises. It looks like the relationship of the premises to the conclusion is irrelevancy. – Mark Andrews – 2019-02-09T03:00:44.227

But this is a joke, right. "The Bruins will win when it snows in Miami" (or whatever city you want to choose where it never snows), meaning, never. And then when it does happen to snow, you can say the above. In other words, the above is not a stand-alone statement, it relies on unspoken premises. – Mr Lister – 2019-02-09T13:22:14.067