If a person thinks that someone will not return his salaam, should he still say salaam?

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As-Salaamu-Alaikum wa Rahmatullahi wa Barakatuh. (May Allah's Peace, Mercy and Blessings be upon all of you)
One of our brothers/sisters has asked this question:
If a person thinks that if he greets someone, that person will most likely not return his salaam, should he still say salaam or not?
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Answer:

Praise be to Allaah.

Yes, he should still say salaam.

Whatever written of Truth and benefit is only due to Allah's Assistance and Guidance, and whatever of error is of me. Allah Alone Knows Best and He is the Only Source of Strength.

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