Topics: Deductive reasoning (predicate logic)
Given
Every student who studies mathematics has passed calculus. [1]
Alex is a student. [2]
Alex studies mathematics. [3]
Everyone who has passed calculus can solve differential equations. [4]
Find
Can Alex solve differential equations?
Solution
Definition:
S(x): x is a student.
M(x): x studies mathematics.
C(x): x has passed calculus.
D(x): x can solve differential equations.
Representation:
[1]: ∀x(S(x)∧M(x)→C(x))
[2]: S(Alex)
[3]: M(Alex)
[4]: ∀x(C(x)→D(x))
Deduction:
Instantiate x=Alex in [1]: S(Alex)∧M(Alex)→C(Alex),
with [2] and [3] we conclude: C(Alex).
Instantiate x=Alex in [4]: C(Alex)→D(Alex),
with C(Alex) we conclude: D(Alex).
Answer
Yes, Alex can solve differential equations.