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Hi @Naqash Ahmed , welcome to Q&A forum!
Per my test, if you use Yes/No column, then the corresponding formula is True and False, like this:
=IF(AND([1st Dose]=TRUE,[2nd Dose]=TRUE),"Vaccinated","Not Vaccinated")
Test Result:
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If you are using Single line of text column, then you can use Yes/No, like this:
=IF(AND([1st Dose]="YES",[2nd Dose]="YES"),"Vaccinated","Not Vaccinated")
Test Result:
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