Police burden for affidavit when requesting a warrant

I understand that Illinois v. Gates (1983) established the "Totality-of-the-circumstances" test for warrant issue based on anonymous police tips. I understand that the burden of investigation is required to verify the legitimacy of the anonymous tip.

My question is about a hypothetical situation where there are 2 anonymous police tips that provide contradictory information. Do the police have the burden of not only proving that one tip IS legitimate or must the police prove the first legitimate and the second as false?

More specifically, if the officer leaves the information out of the affidavit when presented to the judge, is the warrant invalid?

I'm writing a paper on the 4th and am having trouble finding precedent for this situation.

Thanks.