If @strBoolean = 1 BEGIN
    Print 'True'
End else begin
    If @strBoolean= 0 BEGIN
        Print 'False'
    End else begin
        Print 'Null'
    End
End

Time to make a change

We walk in the dark places no others will enter
We stand on the bridge and no one may pass

DECLARE 
    @strBoolean NVARCHAR(1000),
    @strSQL NVARCHAR(1000),
    @bResult BIT = 0

SET @strBoolean = N'(1=1 AND (1=1 OR 2=2))'     --returns 1
--SET @strBoolean = N'(1=2 AND (1=1 OR 2=2))'   --returns 0

SET @strSQL = N'SELECT @bCheck = 1 WHERE '+@strBoolean 
EXEC sp_executesql @strSQL, N'@bCheck INT OUT', @bResult OUT

SELECT 
    (CASE @bResult
          WHEN 1 THEN 'True'
          ELSE 'False'
     END) result