Is "Suppose that _ is true; then _ is true" an incorrect usage of suppose? Is "presuppose" supposed to be used here? [closed]

I'm trying to understand what presuppose means, especially as opposed to "assume".

You'd not start a sentence with 'presuppose'.

• Suppose that A is true. Then B follows.

• Suppose that x is an odd number. Then its square is odd too.

• Suppose that many people disobey the social distancing rules. Then a second wave will occur.

  You rarely use 'presuppose' other than when the contingent truth / state / goal / theory is also stated, and usually first.

• B being true/the case presupposes that A is true.

• Saying that we will eradicate the virus quickly presupposes that an effective and safe antiviral or vaccine will be discovered and tested quickly.

• The permanent presupposes human foresight. [M-W]

• Darwin’s theory doesn’t presuppose any special direction in evolution. [M-W]

'Presuppose that ...' is unidiomatic.

[edit: Thanks to Jason Bassford for pointing out the additional, rarer sense ('assume as an established fact to further build on'), usually taking a that-clause (possibly with 'that' deleted):

• the book presupposes [that] its readers will already know something about the subject (op cit)

but sometimes with a DO:

• The government cannot pass judgment upon or presuppose the illegitimacy of religious beliefs and practices. [op cit] [very formal; legal/political register] ]

but this sense would be unidiomatic with OP's suggested syllogistic sentence.