Solution:
Check with grep -e "searchText1" -e "SearchText2" <FILENAME>

This makes the multiple search possible.

With AND caluse you can use sed option to search.
As :
sed '/pattern/action' filename

for multiple searchs use..
sed -e 'pattern1/p' -e '/pattern2/p' -e '/pattern3/p' FILE

Hope this'll work for you !!
Thanks.