Formula to compare sheets and label as true false

I need to search and compare the information in columns B and C on sheet 1 with column A on sheet 2. I need it to say true or false in column E on sheet 1 if a match is made.

I then need any matched numbers between the 2 to populate column f from sheet 1 with the number from column B in sheet 2.

The final ask is to populate the table on sheet 1 with the corresponding data pulled from above.