Help adding an "OR" (or perhaps "And"?) statement in a long formula string

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How do I add "Free" to the "SEARCH" in R4 for the below scenario:
AND(ISNUMBER(SEARCH("NE",Q5)),ISNUMBER(SEARCH("PRICEPOINT",'Offer Def File'!R4))),

**For IF Q5=PE, there are two options under R4. PE can equal to "Percent OFF" or "FREE".
The full formula string looks like this:
=OR(AND(ISNUMBER(SEARCH("CE",Q5)),ISNUMBER(SEARCH("CENTSOFF",'Offer Def File'!R4))),
AND(ISNUMBER(SEARCH("PE",Q5)),ISNUMBER(SEARCH("PERCENTOFF",'Offer Def File'!R4))),
AND(ISNUMBER(SEARCH("NE",Q5)),ISNUMBER(SEARCH("PRICEPOINT",'Offer Def File'!R4))),
AND(ISNUMBER(SEARCH("NW",Q5)),ISNUMBER(SEARCH("NETWEIGHT",'Offer Def File'!R4))))
Thank you in advance.

 

[Luke M]

We can add it to the Search text, and use an OR statement.
=OR(AND(ISNUMBER(SEARCH("CE",Q5)),ISNUMBER(SEARCH("CENTSOFF",'Offer Def File'!R4))),
AND(ISNUMBER(SEARCH("PE",Q5)),OR(ISNUMBER(SEARCH({"Free","PERCENTOFF"},'Offer Def File'!R4))),
AND(ISNUMBER(SEARCH("NE",Q5)),ISNUMBER(SEARCH("PRICEPOINT",'Offer Def File'!R4)))),
AND(ISNUMBER(SEARCH("NW",Q5)),ISNUMBER(SEARCH("NETWEIGHT",'Offer Def File'!R4))))

 

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Hello Luke,

This worked. Thank you. And thank you for explaining what you did.