Math Logic

[Dumb@Math]

Can anyone please help me? Im stressing out, ive answered some but I’m still paraniod. An explanation with it will be great too!

 

[Subhotosh Khan]

Can anyone please help me? Im stressing out, ive answered some but I’m still paranoid. An explanation with it will be great too!

Since you have answered some - please share those with us, so that we know exactly where would we have to start explaining.

 

[Dumb@Math]

I’ve answered

I.
1. P
2. X
3. P
4. P
5. P

II.
1. p^¬q
2. ¬p^¬q
3. q⇒(¬r)

but I’m unsure of these answers still

 

[Dumb@Math]

I saw error so this is a better pic of the questions from III to IV

 

[pka]

I’ve answered
I. 1. P 2. X 3. P 4. P 5. P

II.
1. p^¬q 2. ¬p^¬q 3. q⇒(¬r)

but I’m unsure of these answers still

Without knowing the exact way your text defines statement it hard to judge the I above. For example some would say the 4 is an X because it in neither true or false.
In II I agree with 1. & 3. But for 2. \(\neg(p\wedge q)\).
As you should, this is the implication truth table:
\(\begin{array}{*{20}{c}}
p&q&{p \to q} \\ \hline t&t&t \\ t&f&f \\ f&t&t \\ f&f&t \end{array}\)
By looking at that table, consider these two statements.
A true statement is implied by any statement.
A false statement implies any statement.

 

[Dumb@Math]

Without knowing the exact way your text defines statement it hard to judge the I above. For example some would say the 4 is an X because it in neither true or false.
In II I agree with 1. & 3. But for 2. \(\neg(p\wedge q)\).
As you should, this is the implication truth table:
\(\begin{array}{*{20}{c}}
p&q&{p \to q} \\ \hline t&t&t \\ t&f&f \\ f&t&t \\ f&f&t \end{array}\)
By looking at that table, consider these two statements.
A true statement is implied by any statement.
A false statement implies any statement.

This is my answer to some, not yet done tho

 

[pka]

This is my answer to some, not yet done tho

\(\begin{array}{*{20}{c}} p&q&r&{p \to q}&{\neg p \to r}&{(p \to q) \vee (\neg p \to r)} \\ \hline
T&T&T&T&T&T \\
T&T&F&T&T&T \\
T&F&T&F&T&T \\
T&F&F&F&T&T \\
F&T&T&T&T&T \\
F&T&F&T&F&F \\
F&F&T&T&T&T \\
F&F&F&T&F&F \end{array}\)