There are more ways for something to be false than to be true. Therefore, negatively phrased statements have more possible ways to be correct. This makes negatively phrased statements seem more likely to be true. 

University of Michigan - Ann Arbor

Bad information is more salient than good information, negative instances attract more attention, negative information is processed more thoroughly, and there are more possible false statements. 

Why negatively phrased statements seem more likely to be true

Jaffé, M. E., & Greifeneder, R. (2020). Can that be true or is it fake news? New perspec- tives on the negativity bias in judgments of truth. In R. Greifeneder, M. Jaffé, E. J. Newman, & N. Schwarz (Eds.), The psychology of fake news: Accepting, sharing, and cor- recting misinformation (pp. 115–130). London: Routledge. 

Can that be true or is it fake news? New perspectives on the negativity bias in judgments of truth

Negativity can be created with two methods: concept valence and negation. Negated statements are more likely to be judged as true. 

-Concept valence: "more than vs. less than"

-Negation: "this vs not this" 

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