Homework help (HAM2)

[Jarvitä]

I know mathematics is the language of physics, but sometimes it feels as though they're putting too much focus on it in my university. I don't even know how to begin solving these problems.


1. Is the following combined logical statement a teutology, contradiction, or neutral? Define the logical values (1 or 0) of the statements A, B and C with which it shall follow that the following combined statement has a logical value of 1, if applicable.

legend:

/\ conjunction
\/ disjunction
=> implication
<=> equivalence

Statement: A \/ (B<=>(A=>C /\ A) \/ B=>C) /\ B

2. Define the numerical limitations of x such that the following non-equation system is arithmetically logically defined.

legend:

|| absolute value
=> greater or equal

System: (||x|- ln x^(1/2)|^(1/3)) / (|(x+1)(x-1)|)=>x^e

If I ever need this in physics (my major), I will consider suicide. :huh:

 

[Urwumpe]

Ah mathematical logic, my favorite (I had to take this subject twice and delay my studies by one year, because the professor did not allow a second chance exam in the same season)

I know mathematics is the language of physics, but sometimes it feels as though they're putting too much focus on it in my university. I don't even know how to begin solving these problems.


1. Is the following combined logical statement a teutology, contradiction, or neutral? Define the logical values (1 or 0) of the statements A, B and C with which it shall follow that the following combined statement has a logical value of 1, if applicable.

legend:

/ conjunction
/ disjunction
=> implication
<=> equivalence

Statement: A / (B<=>(A=>C / A) / B=>C) / B

As it has only three variables (A, B, C) you have to check only 8 combinations. When all eight combinations result in the term being true, it is a tautology, but I have doubts it is.

(0 0 0) -> 0 \/ (0<=>(0=>0 /\ 0) \/ 0=>0) /\ 0
-> 0

etc.

2. Define the numerical limitations of x such that the following non-equation system is arithmetically logically defined.

legend:

|| absolute value
=> greater or equal

System: (||x|- ln x^(1/2)|^(1/3)) / (|(x+1)(x-1)|)=>x^e

If I ever need this in physics (my major), I will consider suicide. :huh:

Uh yes... But actually, you just have to find the interval of x, where the non-equation is valid. For example by dividing by x^e and solving it. Then you have to deal with two symmetric cases: x < 0 and x>0

 

[Jrquinlisk]

2. Define the numerical limitations of x such that the following non-equation system is arithmetically logically defined.

legend:

|| absolute value
=> greater or equal

System: (||x|- ln x^(1/2)|^(1/3)) / (|(x+1)(x-1)|)=>x^e

This one is just asking for the values of x where the function is defined; you don't need to solve it (and I wouldn't want to). Since you're dividing by |(x+1)(x-1)|, you need to make sure that this value doesn't equal zero. Thus, this function is defined for any x ≠ ±1.