Planen er dum.

Planen is made of the noun plan plus the definite ending -en.

• en plan = a plan
• planen = the plan

So Danish often puts the onto the end of the noun instead of using a separate word.

Because in Danish, the definite article is very often a suffix.

In this sentence, planen already means the plan, so no extra word is needed.

A separate definite article such as den is used in other situations, especially when an adjective comes before the noun:

• planen = the plan
• den dumme plan = the stupid plan

So Planen er dum is correct exactly as it is.

Er is the present tense of at være, which means to be.

So it works like English is:

• Planen er dum = The plan is stupid

This is a very basic Danish sentence pattern:

subject + er + adjective

Because dum is a predicate adjective here, meaning it comes after er.

In Danish, predicate adjectives agree with gender and number, but not with definiteness. Since plan is a common-gender singular noun, the adjective stays in the basic form dum.

Compare:

• Planen er dum — common gender singular
• Huset er dumt — neuter singular
• Planerne er dumme — plural

So even though planen is definite, that does not make the adjective become dumme in this position.

You learn it from the dictionary form:

• en plan = common gender
• et would mark a neuter noun

Because it is en plan, the definite singular becomes planen.

If it were a neuter noun, the definite singular would usually end in -et instead.

Not exactly.

In modern Danish, dum usually means:

• stupid
• silly
• foolish

It usually does not mean unable to speak, which is an older meaning of English dumb.

So in Planen er dum, the idea is that the plan is foolish or a bad idea.

You would say:

• en dum plan = a stupid plan
• den dumme plan = the stupid plan

This is useful because it shows the difference between an adjective before the noun and after the verb:

• Planen er dum — the adjective is after er
• den dumme plan — the adjective is before the noun, so it becomes dumme

That change is very common in Danish.

Negative:

• Planen er ikke dum = The plan is not stupid

Yes/no question:

• Er planen dum? = Is the plan stupid?

Danish usually makes yes/no questions by putting the verb before the subject.

Yes. This is the standard pattern for a simple statement:

subject + verb + complement

So here:

• Planen = subject
• er = verb
• dum = complement adjective

It works very much like English The plan is stupid.

Yes, it sounds completely natural.

But dum is definitely negative. About a plan, it can mean something like:

• That plan is stupid
• That’s a silly idea
• That’s a bad idea

How harsh it sounds depends on tone and context, but it is not a mild compliment-like word. It is criticism.