Propositional Logic

[ShadyS87]

I do apologize, my previous post was messed up when I tried formatting it. This is the question

Question 1

Let B be a set with A={n:n∈Z+ and x<16} and p, q and r be three propositions concerning an integer n in A.
p means 'n is an odd number'
q means 'n is a prime number'
r means 'n is less than 8'
a) Find the truth set of the following logical expressions: p∧q; p⊕q; p→q and r→q.
b) Express each of the three following compound propositions using p, q, r and appropriate logical symbols:

• 'n is neither neither odd nor is a prime number'
• 'if n is odd and n less than 8 then n is a prime number '
• 'n is a prime number only if n is odd'
• 'n is a prime number if n is odd'

c) Write in words the contrapositive of the statement given symbolicaly by 'q→p'.

Question 2:
Let p and q be two propositions. Using the laws of propositional logic seen in this topic, show that (p→q)∧p=p∧q.



The first question I believe it would be:

- {1, 3, 5, 7, 11, 23}
- { 2, 9, 15}
- everything in p and q except {9, 15}
- everything in r and q except {2, 4, 6}

I am lost in the the difference between "n is a prime number only if n is odd" and "n is a prime number if n is odd"

The second question honestly I am also stuck.

Also, I wrote
n is neither odd nor is a prime number = ¬ p V ¬ q
if n is odd and less than 8 then is a prime number = (p V R) → q

 

[pka]

I do apologize, my previous post was messed up when I tried formatting it. This is the question
Also, I wrote
n is neither odd nor is a prime number = ¬ p V ¬ q
if n is odd and less than 8 then is a prime number = (p V R) → q

Please, Please ShadyS87, tell Prof Peterson and me some information about you situation.
To be clear, will you tell us the source of this material. Is it class notes and/or textbook.
Do you have a clear list of definitions and axioms to guide you through this material.

Now: I have told you the the neither is a conjunctive(and) not disjunctive(or).
But twice (are more times) you have written n is neither odd nor is a prime number = ¬ p V ¬ q.
It is \(\displaystyle \neg P\wedge \neg Q\). Do you know difference in \(\displaystyle \wedge~\&~\vee~?\)

 

[Shadow123]

How do i show the working for this?