No P is M. All S are M. ∴ No S is P.
No circle is a rectangle. All squares are rectangles. ∴ No square is a circle.
Modus Cesare is the stronger form of the Modus Cesaro, which only infers an existential conclusion.
The name “Cesare” is a mnemonic term that helps to remember the most important characteristics of this mode: The “C” at the beginning indicates that it is related to the Modus Celarent, the “e” and “a” indicate the negative and affirmative universal statements in the premisses and the negative universal conclusion.