Discrete math problem

[always]

Show that (y→x)→x is logically equivalence to x V y

I have tried using truth table and it have worked. I would like some help solving it without using the truth table : I need to show it to be logically equivalence without using truth table.

 

[pka]

without using truth table.
Show that (y→x)→x is logically equivalence to x V y. I would like some help solving it without using the truth table

We know that \((Y\to X)\equiv (\neg Y \vee X)\)
Lets apply that again \((\neg Y \vee X)\to X\equiv\neg(\neg Y \vee X)\vee X\)
Now\( \neg(\neg Y \vee X)\vee X\equiv ( Y \wedge\neg X)\vee X\equiv (Y\vee X)\wedge(\neg X\vee X)\)
Can you finish?

 

[always]

We know that \((Y\to X)\equiv (\neg Y \vee X)\)
Lets apply that again \((\neg Y \vee X)\to X\equiv\neg(\neg Y \vee X)\vee X\)
Now\( \neg(\neg Y \vee X)\vee X\equiv ( Y \wedge\neg X)\vee X\equiv (Y\vee X)\wedge(\neg X\vee X)\)
Can you finish?

no sorry I really can't I'm really bad at proving it to be logically equivalence

 

[pka]

no sorry I really can't I'm really bad at proving it to be logically equivalence

That response is is totally unhelpful. In order to help you, you must explain exactly what about my reply it is that you do not understand,
Start with \(p\to q\equiv \neg p\vee q\). Be complete.

uiv

 

[always]

That response is is totally unhelpful. In order to help you, you must explain exactly what about my reply it is that you do not understand,
Start with \(p\to q\equiv \neg p\vee q\). Be complete.

uiv

Alright, I can't solve it cause I have no clue what to do next.

 

[pka]

Alright, I can't solve it cause I have no clue what to do next.

Please try to be clear in replying .
\((\neg Y \vee X)\to X\equiv\neg(\neg Y \vee X)\vee X\) Do you understand that step?
If not the write a sentence explaining exact why you do not understand the process.

 

[always]

Please try to be clear in replying .
\((\neg Y \vee X)\to X\equiv\neg(\neg Y \vee X)\vee X\) Do you understand that step?
If not the write a sentence explaining exact why you do not understand the process.

Look I only know how to solve it with truth table,that's all. I have no clue how to solve it with the logical equivalence way,cause I have a hard time understanding the important equivalence laws that must be memorized and I don't know how to start.

 

[pka]

Frankly I appears to me that you are in the wrong course of study. Sorry to be so honest with you.

 

[Dr.Peterson]

Look I only know how to solve it with truth table,that's all. I have no clue how to solve it with the logical equivalence way,cause I have a hard time understanding the important equivalence laws that must be memorized and I don't know how to start.

If you want help, you need to help us by telling us what you know that we can use. We aren't going to give you a course in logic from the beginning, so we need a starting point.

Can you tell us what laws you have been taught? Can you make some attempt to find appropriate laws to apply? Can you show us an example you were given and ask specific questions about it that we can discuss? Try to work with us. If you can't, then I'll have to agree with pka.