Question

Which statement is logically equivalent to the following conditional statement?

If it has five sides, then it is not an octagon.

If it is not an octagon, then it has five sides.

If it does not have five sides, then it is not an octagon.

If it does not have five sides, then it is an octagon.

If it is an octagon, then it does not have five sides.

Answer 1

For two statements to be logically equivalent, they must both be true in relation to one another. so wouldnt the answer be c? or am i incorrect?

Answer 2

You are looking for a contrapositive statement.
For example:
If it is nice, then I will go for a walk in the park. (original statement)
is equivalent to
If I do not go for a walk in the park, it is not nice. (contrapositive to the original statement)

Symbolically, it is
\[p->q \equiv ~q->~p\]

Answer 3

* \[p->q \equiv ~q->~p\]

Answer 4

Darn I think you need to type \text{~}
That stinks that it's not showing up normally.

Answer 5

One of those special LaTeX things.

Answer 6

\[\LARGE\rm p\to q \equiv \text{~}q\to\text{~}p\]That's what we were going for, yes? :D

Answer 7

@Elizabeth03
It is not c.
c is the converse of the original statement.
Generally the converse is NOT equivalent to the original statement.

Answer 8

the question still confuses me...and for this question im not looking for the converse im looking for the logically equivalent statement....For two statements to be logically equivalent, they must both be true in relation to one another.

Answer 9

Which statement is logically equivalent to the following conditional statement?

If it has five sides, then it is not an octagon.

If it is not an octagon, then it has five sides.

If it does not have five sides, then it is not an octagon.

If it does not have five sides, then it is an octagon.

If it is an octagon, then it does not have five sides

Answer 10

The original statement is logically equivalent to the contrapositive.
Out of the four choices, there is the converse (C) which is NOT what you're looking for.

Answer 11

it would be d..

Answer 12

There is a contrapositive which is what you should be choosing.

Try and study the example I gave earlier:

For example:
If it is nice, then I will go for a walk in the park. (original statement)
is equivalent to
If I do not go for a walk in the park, it is not nice. (contrapositive to the original statement)

Answer 13

d is correct! :)
It is the contrapositive of the original statement.

Answer 14

Which statement is logically equivalent to the following conditional statement?

If you have unlimited texting, then you will not be charged for overages.

If you are charged for overages, then you do not have unlimited texting.

If you are not charged for overages, then you do not have unlimited texting.

If you have unlimited texting, then you will be charged for overages.

If you do not have unlimited texting, then you will not be charged for overages.

what about this one the same concept....no?

Answer 15

Which one do you think is the contrapositive (i.e. logically equivalent)?

Answer 16

i believe the answer is b....its the opposite

Answer 17

Type in \sim to get \[\Large \sim P\]

Answer 18

Recall:
\[\large{p->q \equiv ~q->~p}\]

Answer 19

Opposite is not enough.
Contrapositive needs both to be opposite, AND the positions reversed.

Answer 20

* I did it again!
recall:
\[p->q \equiv\ \sim q -> \sim p\]

Answer 21

@jim_thompson5910 @zepdrix Thank you both of you.
What does \sim stand for? I usually call \(\sim \) tilda or tilde.

Answer 22

it's used in similarities

P \sim Q

\[\Large P \sim Q\]

and you often see it in geometry (when stating that two triangles are similar)

\[\Large \triangle ABC \sim \triangle PQR\]

it's also a tilde symbol

Answer 23

@jim_thompson5910
Oh.... of course, I should have thought of that! Silly me!
Thank you a bunch!

Answer 24

you're welcome

Answer 25

@Elizabeth03
Have you found the logically equivalent choice? It is not b.
Sorry, I was distracted for a while! :)

Answer 26

\[\lnot\]

Answer 27

\lnot

Answer 28

@satellite73
Thank you. You have just added \(\lnot, \land, \lor \) to my répertoire!