Check my answer to see if I'm right.
Is this statement equivalent? Explain why it's is equivalent?

If you are fishing at 1 p.m., then you are driving a car at 1 p.m.

I think it is equivalent.

Question

Check my answer to see if I'm right.
Is this statement equivalent? Explain why it's is equivalent?

  If you are fishing at 1 p.m., then you are driving a car at 1 p.m.

I think it is equivalent.

anonymous · Answer

yep

juana02 · Answer

can u explain why i am right?

mathmate · Answer

Are there two statements in the question?
Usually we are asked to tell if the two statements are logically equivalent.

mathmate · Answer

Can you post the original question, please?

juana02 · Answer

ok

juana02 · Answer

Determine which, if any, of the three statements are equivalent.
           a.)   If you are fishing at 1 p.m., then you are driving a car at 1 p.m.
            b.)  You are not fishing at 1 p.m. or you are driving a car at 1 p.m.
            c.)  It is false that you are fishing at 1 p.m. and you are not driving a car at 1 p.m.
 A,B,C are separate

mathmate · Answer

Determine which, if any, of the three statements $are$ equivalent.
You need to choose $two$ statements which are logically equivalent, if any.

mathmate · Answer

When you see "if...then", it is a conditional statement, i.e. p$\rightarrow$ q.
When you see "or", most of the time it is a statement of the form $p \lor q$
When you see "and", most of the the time it is a statement of the form $p \land q$.
Can you try to give an answer now?

juana02 · Answer

but its three answer or just one this question confuses me?

juana02 · Answer

@mathmate

mathmate · Answer

The three are not answer choices.
They give three statements, and you are expected to find if there are two that are equivalent.
There could be 4 answer choices, such as:
1. a & b
2. b & c
3 a & c
4 none

But the answer is not yet your preoccupation.  Your first task is to find out how to check if they are equivalent, which goes back to your study of logic operations, $ \lor, \land, \rightarrow, \equiv \Leftrightarrow, \neg, ... $ and truth tables.

Assuming the statements p="fishing at 1 pm", q="driving a car at 1pm"
then since (a) is a conditional statement, (a) becomes 
$p\rightarrow q$

Work on (b) and (c) and see if you can find logical equivalence between the statements.

juana02 · Answer

Ok Let me work on them give me few minutes I will give u the answer to both

juana02 · Answer

A. p→ q.
B.p∨q
C.p∧q
am i right?
now how do I determine if they are true statements or not?

juana02 · Answer

I think these are the answer tell me if im right? 
A. true statement
B. false statement
C. true statement

@mathmate

mathmate · Answer

We do not know if each statement is true unless we actually go fishing or driving.
But we can make a truth table as follows
p q p$\rightarrow$q
T T T
T F F
F T T
F F T
This is a typical truth table for the $\rightarrow$ operator.
You will have to do the same for the other two.
If you find that the truth table (last column) of two cases (out of A, B and C) are identical, then you can say that those two statements are equivalent.

On the other hand, your evaluation of the statements of B and C are not correct.
Read the original statements carefully and see if you can find the correct.  Both B and C have the same cause of mistake.

mathmate · Answer

* find the $corrections.$

juana02 · Answer

Ok C is a false statement because u have to be driving at 1pm to be fishing at 1. But I don't seem to understand why B is wrong but I guess since it's similar to A. Can u explain me why B is wrong?

mathmate · Answer

You cannot declare any of A, B and C true or false, because we don't know if the person went fishing or not, nor driving.

All we can do is to set up a truth table, as I have done for (A), which says,
if p=T, q=T, then p$\rightarrow$q =T
p=T, q=F, then then p$\rightarrow$q =F
p=F, q=T, then then p$\rightarrow$q =T
p=F, q=F, then then p$\rightarrow$q =T
(these values depend on the operator, hope you studied them before).

You need to make the correct statement first for (B) and (C), then construct the truth tables.
Compare the truth table, if $two$ truth tables are the same, then these two statements are equivalent.

For the statements, these are the corrections you need to make before working on the truth tables:
A. p→ q.
B.$\color{red}{\lnot}$p∨q  (You are $\color{red}{not}$ fishing at 1 p.m...)
C.$\color{red}{\lnot}$p∧q ( It is $\color{red}{false}$ that you are fishing at 1 p.m...)

mathmate · Answer

@juana02 
I appreciate your patience to learn step by step, which is what it takes to do math.
I have to go to bed now and I can only continue tomorrow afternoon.  If you need to finish it in a rush, you can make a new post and continue from where you left off.  Otherwise I will be very happy to continue tomorrow!

juana02 · Answer

Im not in a rush I can wait for u to help me tommorrow if you like.

mathmate · Answer

Hi @juana02, have you gone further with the problem?

juana02 · Answer

can u help me?

mathmate · Answer

Yes, where're you at?
Can you first examine the correct translation (into mathematical logic) statements B & C and be convinced that they are indeed correct?

juana02 · Answer

ok

mathmate · Answer

Have you done truth tables before? If not, take a look at this article. http://en.wikipedia.org/wiki/Truth_table with special attention on the operators "not", "and", "or", "conditional", "biconditional" and "equivalent".