Question

hey guys ok I will give a medal if you help me out ! and if ya' want ill fan ya'.
Okay so my question is how do you find the logically equivalent of a statement. I am so confused when it comes to proofs so any help would be fabulous!!!

Answer 1

please help!!

Answer 2

In logic, statements p and q are logically equivalent if they have the same logical content. Does that make sense?

Answer 3

yes but no

Answer 4

Two statements are logically equivalent if they are either both true or both false.

Answer 5

ok.. so just to see if I got it... if I said : If today is a weekday, then it is not Saturday.
the logical equivalent statement to this would be: If today is not a weekday, then it is Saturday. is this right?

Answer 6

Welllll... Kind of. If today is not a week day, it means that it's the weekend, meaning it could be either Saturday or Sunday. So you could say,

If today is a weekday, then it is not the weekend.
If today is not a weekday, then it is the weekend.

Answer 7

ok

Answer 8

Here's another example

Answer 9

If it is raining, then I will bring my umbrella.

This statement is of the form p => q ("p implies q"). In this case,
p is "it is raining"
q is "I will bring my umbrella"

p => q means that if p is true, then q is also true. (That is, "if p, then q").

The converse of the statement is "If I bring my umbrella, then it is raining" (that is, q => p). Note that the converse is NOT logically equivalent to the original statement. The original statement said that if it rains, then I'll have my umbrella, but it didn't say anything about what happens if it doesn't rain. I could very well bring my umbrella every single day, regardless of weather conditions.

The inverse of the statement is "If it doesn't rain, then I won't bring my umbrella" (that is, not p => not q). The inverse is also NOT logically equivalent to the original statement. However, the converse and inverse are logically equivalent to each other.

Lastly, the contrapositive "If I don't bring my umbrella, then it isn't raining" (that is, not q => not p) IS logically equivalent to the original statement.

Answer 10

hmm ok it makes more sense now, do you think you could give me one to try out?

Answer 11

Ok, I'll give you two, one of them is logically equivalent and one is logically inequivalent

Answer 12

ok

Answer 13

If jeff passes math then he will be happy
jeff passes math and he is happy

If jeff passes math then he will be happy
if jeff is not happy then he did not pass math

Answer 14

Which one of these are logically equivalent?

Answer 15

is it the second one idk

Answer 16

Yep! You're right, good job :)

Answer 17

yay!

Answer 18

So you understand now, yeah? :)

Answer 19

yes I do thank you so much lol

Answer 20

You're very welcome. Good luck with your studies

Answer 21

thanks :)