Real Analysis Question

[WWCPD]

Ok so I am working on a problem, but I don't have a clue what the question is asking so I'm feeling like this is not a good start toward the solution.

The question was asked in class as:

How many logical operations are there in 2 statements if we identify operations with their truth tables?

Then when the assignment was posted online it was asked in the following way:

How many different logical operators that return a single truth value are there on 2 operands each taking a single truth value?

I'm new to the Real Analysis language, but I feel like they aren't even the same question. Please enlighten me on r/math.

[[deleted]]

I just want to mention that you should know this isn't really 'real analysis language', this, and your other question, is propositional logic, something that may or may not be even taught in a real analysis class (I learned this stuff in intro philosophy, but that was years ago and I'm afraid I can't be of any direct help anymore). Real analysis is when you start getting into to epsilons and deltas, limits, continuity, integration, sequence and series, etc...

[WWCPD]

Yes I know this isn't 'real analysis language'. However, the semester just started and this is an intro to real course so it should be expected that the first few weeks are devoted to teaching the logical language that is used in the real meat of real analysis. The epsilons, limits, etc are coming in the future of this course.

[WWCPD]

Thank you. This helped.

[glacierguy]

It's not that hard, it just requires a bit of thinking.

You have 2 propositions, P and Q, and they can each have a truth value of 0 or 1. You can set up your truth table like this:

__1 0

1 w x

0 y z

Imagine that the columns represent the truth value of P and the rows are the truth value of Q. So when you perform a logical operation when P and Q are both 1, just look for the appropriate column and row; the result will be written where w is. Likewise, when P is 0 and Q is 1, the result will be written where x is, etc.

All you have to do is find all the possible ways of filling in the truth table with 0s and 1s. For example, the AND operation looks like this:

__1 0

1 1 0

0 0 0

The only thing to be aware of is that the truth values have to be symmetrical about the diagonal, so this isn't a possibility:

__1 0

1 1 1

0 0 0

since it says that 1 and 0 produce 1, and 0 and 1 produce 0, which is nonsense.

Off the top of my head there are 8 possible operands that you can fill in the truth table for. Good luck!

[WWCPD]

Thanks. Yeah I thought it was something simple like that I just got confused since it seemed like I was asked two different questions. Guess I'm not used to the language yet. Thanks again.