Kennarinn segir að taflan sé gagnleg, en gamli hlekkurinn sé gagnslaus núna.

Sé is the present subjunctive form of vera (to be), while er is the ordinary present indicative.

In a sentence like this, Icelandic often uses the subjunctive in a subordinate clause after segir að (says that), especially in reported statements or more formal/written style:

• Kennarinn segir að taflan sé gagnleg
  = The teacher says that the board/chart is useful

So the sentence is presenting what the teacher says, not directly asserting it as the speaker’s own plain statement.

In everyday speech, you may also hear er in similar contexts, but sé is very common and important to recognize.

Sé is a form of vera (to be).

More specifically, it is:

• 3rd person singular present subjunctive
• used here with both:
  • taflan (the board/chart)
  • gamli hlekkurinn (the old link)

So:

• taflan sé gagnleg
• hlekkurinn sé gagnslaus

Both subjects are singular, so sé fits both of them.

Because the second clause is coordinated with the first one by en (but), and both are still understood as depending on segir að.

So the structure is basically:

• Kennarinn segir að [taflan sé gagnleg], en [gamli hlekkurinn sé gagnslaus núna].

You could think of it as:

• The teacher says that the board/chart is useful, but that the old link is useless now.

In English, the second that is often omitted too, so this works similarly.

That is the suffixed definite article in Icelandic. Instead of usually putting a separate word like the before the noun, Icelandic often adds the article to the end of the noun.

Examples from the sentence:

• kennari = teacher
  kennarinn = the teacher

• tafla = board / chart / table
  taflan = the board / the chart / the table

• hlekkur = link
  hlekkurinn = the link

So Icelandic often expresses the as part of the noun itself.

Because gamli is the weak adjective form, which is normally used when the noun is definite.

Compare:

• gamall hlekkur = an old link
• gamli hlekkurinn = the old link

This is a very important Icelandic pattern:

• indefinite noun → adjective usually in a strong form
• definite noun → adjective usually in a weak form

So since hlekkurinn means the link, the adjective becomes gamli.

Because gamli is an attributive adjective: it comes directly before the noun:

• gamli hlekkurinn = the old link

But gagnleg and gagnslaus are predicate adjectives: they come after vera (to be):

• taflan sé gagnleg
• hlekkurinn sé gagnslaus

Predicate adjectives behave differently. They agree with the subject, but they do not take the same weak-form pattern just because the subject is definite.

So:

• gamli hlekkurinn → adjective before a definite noun → weak form
• hlekkurinn sé gagnslaus → adjective after to be → predicate form

That difference is very common in Icelandic.

They agree in gender, number, and usually case with the subject.

Here:

• taflan is feminine singular nominative
• so the adjective is gagnleg

And:

• hlekkurinn is masculine singular nominative
• so the adjective is gagnslaus

This may look a little confusing because not all adjectives show gender in the same way.

For example:

• gagnlegur = masculine
• gagnleg = feminine
• gagnlegt = neuter

But with gagnslaus, the masculine and feminine nominative singular are the same:

• gagnslaus = masculine
• gagnslaus = feminine
• gagnslaust = neuter

So the agreement is there, even if the ending does not always make it obvious.

It can mean either, depending on context.

• hlekkur can be a link in a chain
• it can also be a hyperlink / web link

In this sentence, gamli hlekkurinn most naturally sounds like the old link in the digital sense, especially because calling a link gagnslaus núna (useless now) fits internet links very well.

Núna means now.

So:

• gamli hlekkurinn sé gagnslaus núna = the old link is useless now

It tells you that the link is useless at the present time, which can imply that it may have worked before.

Word order with núna is fairly flexible in Icelandic, but putting it at the end is very natural.

Not necessarily. Tafla can mean several things depending on context, such as:

• board
• chart
• table
• sometimes other related meanings

So if the meaning has already been given to the learner, that context decides it. Grammatically, though, the important thing is that tafla is a feminine noun, which is why the adjective appears as gagnleg.

Yes. It is very typical.

You have:

• a main clause: Kennarinn segir
• followed by a subordinate clause introduced by að
• then a second coordinated subordinate clause with en

So the pattern is:

• [Main clause] + að + [subordinate clause], en + [parallel subordinate clause]

This is a normal, useful structure for reporting what someone says or thinks:

• X segir að ...
• X heldur að ...
• X veit að ...

So this sentence is a good example of several core Icelandic patterns at once:

• the suffixed definite article
• adjective agreement
• weak adjective forms before definite nouns
• the subjunctive in a subordinate clause