Are the following statements logically equivalent?
p ⋁q ⋀ r ; p ⋁(q ⋀ r) ;

Question

Are the following statements logically equivalent?
p ⋁q ⋀ r   ; p ⋁(q ⋀ r)   ;

anonymous · Answer

Thank you so much you have no idea as to how much help this is.

anonymous · Answer

i don't know :(

anonymous · Answer

@FutureMathProfessor    he might know

anonymous · Answer

Not equivalent

anonymous · Answer

thank you 
can you tell me why

anonymous · Answer

Ok this is VERY abstract so if you still don't understand, I'm sorry. This is stuff college students struggle with.
Think of q ⋀ r as the "overlapping" portion between the two, as in, values that are common in both sets q and r
If we follow through with that operation first (hence the parentheses, then we will include all of our result with everything in set p (that's where the v comes in)

If we took out the parentheses, we would first include ALL values in sets p and q, and then we would find the overlapping portion between ALL OF THESE VALUES and r. This would be substantially less than the other one, as we would be throwing out many more values when we overlap our solutions with set r (^)

anonymous · Answer

Thank you

anonymous · Answer

Were you forced to take discrete math?

anonymous · Answer

yes I was

anonymous · Answer

Does that make sense how I wrote that or no?

anonymous · Answer

yes it does

anonymous · Answer

Great :)