If between two اِسْمٌ  there is a relation of possession, then possessed is called مُضَافٌ  and the possessor is مُضَافٌ إِلَيْهِ 

مُضَافٌ and مُضَافٌ إِلَيْهِ always come one after another. مُضَافٌ never comes with ال and ‘tanwin’ and مُضَافٌ إِلَيْهِ is always مَجْرُوْرٌ , example-

meaning

مُضَافٌ إِلَيْهِ

مُضَافٌ

Relation of word

Hamid’s pen

حَامِدٍ

قَلَمُ

قَلَمٌ + حَامِدٌ

house of a businessman

تَاجِرٍ

بَيْتُ

بَيْتٌ + تَاجِرٌ

house of the businessman

التَّاجِرِ

بَيْتُ

بَيْتٌ + التَّاجِرُ

sustainer of mankind

النَّاسِ

رَبُّ

رَبٌّ + النَّاسُ

house of Allah

اللهِ

بَيْتُ

بَيْتٌ + اللهُ

name of the teacher

الْمُدَرِّسِ

اِسْمُ

اِسْمٌ + الْمُدَرِّسُ

the door of the garden

الجَنَّةِ

بَابُ

بَابٌ + الجَنَّةُ

leaf of the tree

الشَّجَرَةِ

وَرَقَةُ

وَرَقَةٌ + الشَّجَرَةُ

knower of invisible

الغَيْبِ

عَالِمُ

عَالِمٌ + الغَيْبُ

 

If an ism has تَنْوِيْنٌ then it is indefinite and if it has ال then it is definite. But have you noticed that the mudaf don't have ‘al’ and ‘tanween’ on it. So how to determine whether it is definite or indefinite?

مُضَافٌ can be both definite and indefinite depending on the state of مُضَافٌ إِلَيْهِ . If مُضَافٌ إِلَيْهِ is definite theمُضَافٌ is definite, as in 1st line   قَلَمُ is definite because Hamid is definite but in 2nd line بَيْتُ indefinite as a businessman is indefinite.

example from Quran (only to understand uses of مُضَافٌ)  

night of qadr is greater than a thousand months

لَيْلَةُ الْقَدْرِ خَيْرٌ مِّنْ أَلْفِ شَهْرٍ

and the consequence of evil is definitely evil

وَجَزَاءُ سَيِّئَةٍ سَيِّئَةٌ مِّثْلُهَا

then if one does good, even as tiny as an atom, he will be able to see it.

فَمَن يَعْمَلْ مِثْقَالَ ذَرَّةٍ خَيْرًا يَرَهُ

say, I am asking refuge from the sustainer of mankind

قُلْ أَعُوذُ بِرَبِّ النَّاسِ

Have you not seen, [O Muhammad], how your Lord dealt with the companions of the elephant?

أَلَمْ تَرَ كَيْفَ فَعَلَ رَبُّكَ بِأَصْحَابِ الْفِيلِ

 

Example from Hadith

Duniya is the jail for mumin and heaven for the kafir.

الدُّنْيَا سِجْنُ الْمُؤْمِنِ وَجَنَّةُ الْكَافِرِ

It is compulsory for every Muslim to acquire knowledge.

طَلَبُ الْعِلْمِ فَرِيضَةٌ عَلَى كُلِّ مُسْلِمٍ

 

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