Basic Discrete Math Question: Understanding Conditional Statements

In summary, the student is trying to understand why 1+1=3 but doesn't understand why it would still be true if only half of it is true. The teacher explains that the statement is true if the logic is true, which is something the student was not aware of.
  • #1
MarcL
170
2
Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major

1. Homework Statement

"If 1+1=3 then 2+2=4"

Homework Equations


We just covered conditional statement and its truth table that states if p is false and q is true, then the statement is still true

The Attempt at a Solution



Basic question, following the table given to us, but it doesn't makes sense to me. If 1+1=3 then 2+2=4 , how can the whole statement be true?
 
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  • #2
MarcL said:
Before I make a fool of myself let me just say I just had my first class today and the book/ teacher aren't helpful in my question. And I'm not even sure I'm in the right section, this is just my major

1. Homework Statement

"If 1+1=3 then 2+2=4"

Homework Equations


We just covered conditional statement and its truth table that states if p is false and q is true, then the statement is still true
Yes
MarcL said:

The Attempt at a Solution



Basic question, following the table given to us, but it doesn't makes sense to me. If 1+1=3 then 2+2=4 , how can the whole statement be true?
To quote what you wrote above,
if p is false and q is true, then the statement is still true
 
  • #3
WHat I was trying to say is that, it doesn't make sense to me ( how i see it ) that if I state 1+1 = 3 then 2+2=4 then why would the whole statement be true if only half of it is in realitiy.
 
  • #4
MarcL said:
WHat I was trying to say is that, it doesn't make sense to me ( how i see it ) that if I state 1+1 = 3 then 2+2=4 then why would the whole statement be true if only half of it is in realitiy.
To re-quote what you wrote above,
if p is false and q is true, then the statement is still true
p: 1 + 1 = 3 (false)
q: 2 + 2 = 4 (true)
##p \Rightarrow q## (true)

From the truth table for an implication, the only pair of values of p and q that make the implication false are when p is true and q is false. All other pairs of values for p and q yield a true implication.
 
Last edited:
  • #5
I think the important point is being missed.
Let S be the statement "if p then q". If it turns out that p is false then the statement S is true regardless of whether q is true.
Thus "if 1+1=3 then 2+2=9" is also a true statement.
To put it in everyday language, if you start from a false premise then you can deduce anything.
It is possible that the questioner wants you to illustrate this by a chain of argument that starts with "1+1=3" as a given and ends with "2+2=4". Or, better, ends with "2+2=9".
Here's how you could do the last one:
1+1=3
2+2 = 1+1+1+1 = (1+1)(1+1) = (1+1)2 = 32 = 9
 
  • #6
haruspex said:
It is possible that the questioner wants you to illustrate this by a chain of argument that starts with "1+1=3" as a given and ends with "2+2=4".
I could be wrong, but that's not my take on this problem, which is to recognize that p (1 + 1 = 3) is false, so no matter what q is, the overall implication is true.
 
  • #7
Mark44 said:
I could be wrong, but that's not my take on this problem, which is to recognize that p (1 + 1 = 3) is false, so no matter what q is, the overall implication is true.
Yes, I said it was just a possibility. Without seeing the original question verbatim it's hard to know.
But the main point I wanted to make is that this
MarcL said:
if p is false and q is true, then the statement is still true
is misleading by being insufficiently general. It should say
if p is false then the statement is true regardless of the truth or falsehood of q​
 
  • #8
MarcL said:
Basic question, following the table given to us, but it doesn't makes sense to me. If 1+1=3 then 2+2=4 , how can the whole statement be true?

The truth of the statement is based on the truth or falsehood of the logic, not the parts. The logic is ##p \implies q##. If p is not true, then the logic is true by virtue of the fact it cannot be proven false. There is a large gap between true and useful logic. This logic is true but totally useless, since p is never true.
 

Related to Basic Discrete Math Question: Understanding Conditional Statements

1. What is discrete math?

Discrete math is a branch of mathematics that deals with discrete objects and structures. It is primarily concerned with counting and combinations, and is used in computer science and other fields to solve problems involving finite or countable sets.

2. What are the basic concepts in discrete math?

The basic concepts in discrete math include sets, functions, relations, graphs, and combinatorics. These concepts are used to analyze and solve problems related to discrete structures and objects.

3. How is discrete math used in computer science?

Discrete math is used in computer science to design and analyze algorithms, data structures, and computer networks. It is also used in coding theory and cryptography to ensure secure communication and data storage.

4. What are some real-life applications of discrete math?

Discrete math has various real-life applications, such as in scheduling, inventory management, and optimization problems. It is also used in economic and financial models, as well as in genetics and biology to analyze and model complex systems.

5. Is discrete math difficult to learn?

Like any other branch of mathematics, discrete math may seem difficult at first, but with practice and a solid understanding of the basic concepts, it can be mastered. It is important to have a strong foundation in algebra and logic to understand and apply the concepts of discrete math effectively.

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