Math Is Fun Forum

atran

Member

Registered: 2013-07-12

Posts: 91

Conditional Statement

Hi,

What does it mean for a conditional statement to be true or false?
Here's an example, let p="You pass the test" and q="I buy you a car."
p=>q is obviously a conditional statement, but I don't understand the meaning of it being true or false.

A false statement for me is a statement that is not true (or is a lie).
It's not making sense for me to tell that a conditional statement is a lie (or false).

Can someone help me?
Thanks in advance.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statement

hi atran

Simply that q may not follow from p.

eg.  p = MIF forum members

q = really brainy person

Whilst there are many cases of forum members who are also brainy, the one does not imply the other.  After all it only needs one counter example.

Please don't ask me to suggest one. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Conditional Statement

I can suggest several members without even blinking. They are all the same person, though.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

atran

Member

Registered: 2013-07-12

Posts: 91

Re: Conditional Statement

That sounds like an argument:
1. "MIF forum members" => "really brainy person"
2. there is one member who is not brainy
Therefore, "MIF forum members" does not imply "really brainy person"

Let p="It's raining" and q="It's cloudy" and say p=>q. Semantically, I understand the conditional statement, but I can't understand when one makes a truth table for a conditional. If p is true (i.e. it's raining) and q is false (i.e. it's not cloudy), then the implication is false, so as you said it means that q (being false) does not follow from p.

Now is there a general explanation for unspecified statements p and q: an explanation for why q cannot follow from p when q is false and p is true? If p is false, does that mean, whatever the value of q, that q always follows from p? Is there an alternative word for "follows" since people may also say a conclusion "follows" from a set of premises (as in the latter case the word "follows" refers to logical implication, and in the former case "follows" refers to material implication)?

Thanks for help.

Last edited by atran (2013-11-24 07:36:37)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statement

hi atran

Have a look at

http://en.wikipedia.org/wiki/Material_conditional

By definition all statements must be either true or false*.  A conditional statement is no different.  It may be false.

If it is true then q follows logically from p as in

"x + 7 = 9" => "x = 2"   This is regarded as a piece of TRUE mathematics.

Unlike this

"63 x 0 = 41 x 0" => "63 = 41"

This time the conditional is false because it is not permitted to divide by zero.

Generally, when mathematicians write out a series of logical steps in a proof they hope they have avoided such errors.  Sadly, this is not always the case. 

* Although it is a requirement that a statement must be either true or false, it may not always be possible to say which, as in the Goldbach conjecture http://en.wikipedia.org/wiki/Goldbach%27s_conjecture

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

atran

Member

Registered: 2013-07-12

Posts: 91

Re: Conditional Statement

Hi again,

In the recursive definition of a set, for example:
1) 4∈A
2) If x∈A, then x+1∈A
3) nothing else is in A

Why the step two uses a conditional statement rather than a biconditional one?
I need help with this, thanks...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Conditional Statement

hi atran

With the conditional the set becomes {4,5,6,7,8,9...........}

If you had a biconditional then 4 in A would imply 3 in A would imply 2 in A .....

so we'd end up with {.....-1,0,1,2,3,4,5,6,7,8,9,.........} which is not what was wanted.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Conditional Statement

Let me explain conditional statement via set arguments.

If you know A is true for sure, and you can immediately infer that B is true.
A is true is sufficient condition that B is true.
We can also say that the event A is true is contained in the event B is true.
Like you are in London implies that you are in UK. But the other way around is not necessarily true.

and we can say B is necessary condition for A, for notB is in notA - you are not in UK so you are not in London.

Hope this theory make your logic class a lot easier!

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X'(y-Xβ)=0