Help with logic exercises

  • Thread starter shinghan
  • Start date
  • #1
2
0
I'm having some troubles about some exercises regarding my first year logic course.

1) Deriving (P -> Q) \/ (Q -> R) and showing that this statement is a tautology without using truth tables or venn diagrams.

So far I have no clue on how to start this question. From what I remember in class, a tautology is a statement that is true for all domains and predicates.

2) Deriving P <-> P /\ (P \/ R) without using truth tables or venn diagrams and without using the absorption method.

P <-> P /\ (P \/ R)
P /\ (Q \/ ~Q) <-> (P /\ P) \/ (P /\ Q) identity (left) distributive (right)
<-> P \/ (P /\ Q) idempotency (right)

Thats as close as I can get, but I'm still stuck. I was trying to get both sides similar.

3) Four classmates (William, Xavier, Youssef and Zachary) were suspected of cheating on their homework. At separate meetings with their instructor, they said the following:

William: If Xavier cheated, so did Zachary.
Xavier: William cheated, but Zachary did not.
Youssef: I did not cheat, but at least one of William or Zachary did.
Zachary: If William did not cheat, then Youssef did.

Let W represent the statement: William cheated"
X represent the statement: Xavier cheated"
Y represent the statement:Youssef cheated",
Z represent the statement: Zachary cheated"

and note that each student either cheated or they did not cheat.

(a) If each student is telling the truth, which student(s) cheated?
(b) If the students who cheated did not tell the truth at the meeting, and the students who did not cheat
did tell the truth, which student(s) cheated?
To answer the questions, you may nd it helpful to express each students' statement using a logical expression.
Do not use truth tables
 

Answers and Replies

  • #2
38
0
So, if you're not allowed to use truth tables explicitly, what tools can you use? Did your course define any axiom system for propositional calculus?
 
  • #3
Bacle2
Science Advisor
1,089
10
Can you use the equivalence P-->Q == ~P \/Q ?
 

Related Threads on Help with logic exercises

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
10
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
1
Views
688
  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
0
Views
6K
Top