Question

Use rules of inference to show that the hypotheses “Every student in Computer science major needs to take CSCI1000,” “Every student who takes CSCI1000 knows how to program in JAVA” imply the conclusion “Every student in Computer science major knows how to program in JAVA.”

Answer 1

Premises:

S: x is a student = S(x)

C: S(x) is in Computer Science major = C(S(x))

T: S(x) takes CSCI1000 = T(S(x))

J: S(x) knows how to program in JAVA : J(S(x))

Hypothesis: Every student in Computer science major needs to take CSCI1000,”  “Every student who takes CSCI1000 knows how to program in JAVA”

Hypothesis can be written as C(S(x)) -> T(S(x)) , T(S(x)) -> J(S(x))

Hypothetical Syllogism : If p->q and -> r then p->r

So C(S(x)) -> T(S(x)) , T(S(x)) -> J(S(x)) implies C(S(x)) -> J(S(x))

So we can say Every student in Computer science major knows how to program in JAVA.”