status: DONE
created: 2024-01-16T21:03
updated: 2024-06-11T01:14
Discrete-mathematics-Assignment-3
a)
b)
c)
Step2 is wrong: Step 2 should be Existential instantiation using(1)
Step6 is wrong: Step 6 can't be Universal generalization
P: a is a multiple of 4
Q: 3a+1 is odd
a)Direct proof:
b)Contradiction:
c)Contraposition:
It's clear that
If
If
Basis step: P(1):
Induction Hypothesis: Assume P(k-1) is true
Inductive Step:
Basis step: P(0):
Induction Hypothesis: Assume P(k) is true
Inductive Step: