Is this conclusion logically valid?

Question

Premise 1: No home cooked food is good

Premise 2: No good food is wasted

Conclusion: No home cooked food is wasted.

Not sure if this is logically valid or not and why? Thanks!

Answer 1

• Premise 1: No home cooked food is good.
• Premise 2: No good food is wasted.
• Your conclusion: No home cooked food is wasted.

There are three possibilities given the two premises. Graphically through Venn-diagrams:

Your conclusion isn't necessarily false, as the top Venn-diagram shows, but it does not logically follow, as the bottom 2 Venn-diagrams show.

Answer 2

The conclusion doesn't follow from the premises. Note that doesn't necessarily imply that the conclusion is false.

It would logically follow if you had written it this way:

Premise 1: ALL home cooked food is good.
Premise 2: No good food is wasted.
Conclusion: No home cooked food is wasted.

In this way, if the two premises are true, the conclusion must be true. With your example, the conclusion could be either true or false (i.e. even though No home cooked food is good, they still might not waste it [the bad food]).