Sociology quiz Political science teacher Mr. Jones asks his students to study how social media can influence public opinion by "following" famous activists, academics, and politicians on Twitter. While reading and exchanging each other's Tweets, some classmates became close friends. The first is an example of the project's function, the second is an example of the project's function.

Manifest; latent.

Explanation:

The manifest and latent function are the social scientific concepts theorised by Robert K. Merton in 1949 in his book titled 'Social Theory and Social Structure.'

Manifest functions can be defined as those functions that are performed intently and deliberately. The purpose of these actions is to benefit the society.

In the given case, the first example, that is, Mr Jone's asking his students to study the effects of social media on public opinion is an example of manifest function. It is because the actions performed or ordered were given purposely and with the intent to study the effects of social media on public opinion. And the purpose of the study is to benefit the students to help them understand the psychological effect of social media and be aware of it. Thus, it is an example of a manifest function.

Latent function, on the other hand, can be defined as those actions that are performed unintentionally and accidental. Still, the result of these actions benefits the society.

The second example, in the given case, of some classmates becoming friends because of exchange of each other's Tweets is of the latent function. It is an example of a latent function because these actions were unintentional and accidental. They became friends while sharing each other's Tweets of the study which produce a result of benefit to the students as they got friends. Thus, it is an example of the latent function.

So, the correct answers are manifest and latent.