Google Sheets: OR logic not working in Filter function

I am using OR logic in a filter function using the + operator to filter rows for which the start date or end date falls in a specific month. However, no matches are found in the filter evaluation.

Sheet image=> (https://i.sstatic.net/AJ749hw8.png)

Details:Project Name, start date, and end date are in columns A, B & C.Columns E-H have month number in row 1 and month name in row 2.

The filter formula is in E3:H3 and is as follows:

FILTER($A$2:$A$5,MONTH($B$2:$B$5)=E1+MONTH($C$2:$C$5)=E1)

I want the filter to return projects that will be active in a particular month i.e. either start date, end date, or both falling in that month.