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simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Some conditional statements

A little context:
Statement: p ⟹ q
Converse: q ⟹ p
Inverse: not p ⟹ not q
Contrapositive: not q ⟹ not p

The complex statement is "If x^2 > 10, then x > 0."
7. "x = - 4" would be an example of a
a. converse
b. counterexample
c. contrapositive
d. counterintuition
e. counterpositive
f. counter

The complex statement is "Cars can take you everywhere."
10. "A car can't take you to the moon" would be the
a. converse
b. countermove
c. contrapositive
d. counterexample
e. counterpositive
f. counter

The complex statement is "Baseball players are athletes."
13. Which of the following is accurate?
a. the inverse of the statement is "If someone is a baseball player then someone is an athlete."
b. the statement is "If someone is an athlete, then they are a baseball player."
c. the statement can never be true.
d. baseball players all have great teeth and gums.
e. the inverse of the statement is not true.
f. the converse is: "Joey is a baseball player, and he is not an athlete."

Thank you!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Some conditional statements

hi simonmagusflies

Welcome to the forum.

Questions from this worksheet have been posted before.  I'm not surprised you are asking for help, as some of the questions are bizarre.

In all my years as a mathematician I have never met the term 'counterpositive'.  And I did a logic course as part of my University degree.

I googled it and, despite spending 10 minutes chasing around the internet, I could find no definition of the concept.  Presumably, you were given one as part of the course, so please benefit us all by posting what the term means. Thanks!

Luckily, I don't think we need it here.

The complex statement is "If x^2 > 10, then x > 0."

7. "x = - 4"

I'm sure you know that positive numbers have a negative square root in addition to the positive root, so you ought to be thinking 'This statement isn't true'.  If you can supply an example that proves this then you have a counter example.

definition of counterexample: An example that disproves a statement (shows that it is false).

The complex statement is "Cars can take you everywhere."
10. "A car can't take you to the moon"

Can cars take you everywhere? I can think of loads of places you cannot get to in a car.  The Moon is a pretty good example showing this is false.  So what do you think this is classified as?

The complex statement is "Baseball players are athletes."

Statements don't have to be true in logic theory.  Let's suppose I know that x = 7.  The statement 'If x = 3 then x^2 = 9' is TRUE even though I know that x isn't 3.  The conclusion is valid nevertheless.  So it doesn't matter if you have a poor view of baseball players and disagree with the complex statement.  For the purposes of the question we can proceed anyway.

a. the inverse of the statement is "If someone is a baseball player then someone is an athlete."

This is not an inverse statement.  It's not even a rewording of the original.

b. the statement is "If someone is an athlete, then they are a baseball player."

No it isn't.  There are plenty of athletes who aren't baseball players.

c. the statement can never be true.

Oh yes it can!  Just machine gun all the baseball players that aren't athletes and you've made it true.
Note: I'm a peace loving man so this is just a thought experiment!

d. baseball players all have great teeth and gums.

Irrelevant!

e. the inverse of the statement is not true.

I think the inverse statement is 'If someone is an baseball player, then they are not an athlete.

I'm sure we can easily find counter examples to this so it's not true.  So I think this is a contender for the required answer.  My only worry is where do we get a counter example 'within the information given'.  It's not there so strictly we haven't enough information for this conclusion.

f. the converse is: "Joey is a baseball player, and he is not an athlete."

For the implication P → Q, the converse is Q → P.  So for the given statement the converse is 'If someone is an athlete, then they are a baseball player.  That's not what f says so we can reject that too.

So I'm left with e as the best.

Bob

---

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

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Some conditional statements

Hello, Bob. There is no meaning given in the lesson for "counterpositive". I think it's just there to throw students off.

7. Counterexample? Since it disproves the statement.

10. Another counterexample, I think.

13. Yes, my mom said e as well.

Thank you!