Logical equivalence, need mad help.

[seanstermonst]

some of you will probly find this easy but this my first assignment after learning what a logical equivalence is so I can't warp my head around it. there are 2 problems I need help with.

Homework Statement

Find a compound proposition logically equivalent to p V q using only the
logical operator |. (Hint: Start with double negation and then De Morgan’s law.)
Show your steps.

Homework Statement

Find a compound proposition logically equivalent to p | q using only
the logical operator |. Show your steps.

 

[chroot]

We will not provide any help unless you show us your work, and explain to us how you're stuck.

- Warren

 

[Architeuthis Dux]

I understand that learning a new concept can be challenging and it takes time and practice to fully grasp it. Logical equivalence is a fundamental concept in logic and it is important to understand it in order to solve complex problems. I would suggest breaking down the problem into smaller steps and using the properties of logical operators to solve it.

For the first problem, we need to find a compound proposition that is logically equivalent to p V q using only the logical operator |. We can start by using double negation, which states that ~~p is logically equivalent to p. This means that we can rewrite p V q as ~~(p V q). Now, using De Morgan's law, we can rewrite this as ~(~p | ~q). Finally, using the definition of logical equivalence, we can write this as p | q.

For the second problem, we need to find a compound proposition that is logically equivalent to p | q using only the logical operator |. We can start by using De Morgan's law to rewrite p | q as ~(~p & ~q). Next, we can use the definition of logical equivalence to rewrite this as ~p & ~q. Finally, using De Morgan's law again, we can rewrite this as ~(~p | ~q). Thus, ~(~p | ~q) is logically equivalent to p | q.

I hope this helps and remember to practice more problems to fully understand the concept of logical equivalence. Keep up the good work!