Study for Quiz 2a (2.1 – 2.2)
Oct 17th, 2011 by corricelli
Hello,
Feel free to use this section to study collaboratively for Thursday’s quiz.
Happy studying,
Mrs. Corricelli
15 Responses to “Study for Quiz 2a (2.1 – 2.2)”
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Can you write a conservse to a statement even if it then makes the statement untrue?
I’m still alittle confused on how to do a counter example. I was looking through my notes reviewing and one of the examples we did doesnt make sense to me. The example was if x (squared)=25 then x=5. We said that the answer was x= -5 because that would make the hypothesis true and the conclsion false. But wouldnt it make the conclusion true as well? because -5 squared equals 25.
Libby,
Its not that the answer is -5. Both x = 5 and x = -5 are answers to the equation x(squared) = 25. So when a conditional says, if x(squared)=25 then x=5 it is like a REALLY FORMAL DECLARATION – saying IF x(squared)=25, then THAT MEANS x HAS TO BE 5. (BOLD = yelling). A lawyer or someone who loves to argue would have an issue with that…. they would have to bring up the counterpoint (or counterexample) that x COULD BE -5. When we say x=-5 is a counterexample, that means that we found an example where the hyp is true and the concl (what the conditional claimed HAD to follow the hyp) just is not there – it is not true.
Hope this helps,
Mrs. Corricelli
When you write a biconditional statement, do you always use “if and only if”? Is IFF what makes it a biconditional statement?
Kerry,
Yes and No. If a statement is a definition, then the fact that it is a biconditional is implied (no IFF needed).
Happy studying,
Mrs. Corricelli
for example 1 that you gave today in class, i was confused with counterexamples being false. We had AB=5, with A=10 and B=15..and then we said false, and said that A=-5 and B=0, but this still doesn’t work…therefore, for this, i remember you saying that the hypothesis doesn’t have to be correct, but the conclusion does, so the “new” AB (A=-5 and B=0) are false, which means that this part of the problem is the hypothesis?..and then to further solve the problem we have to find the counterexample if the converse is false? is that correct?
Amy,
I defer to Rosalynn. Her response was great!
Great question,
Mrs. Corricelli
I know you said not to worry about inverse and stuff, but would we have to know how to do it on the CAPT?
No. It is also not on SATs or SAT II’s. The next time you would see it is in a logic course in college.
Good post,
Mrs. Corricelli
amy for example 1 the distance of AB=5units. A=10units and B=15units. the statement is false because there is nothing telling us that it is true. in a counterexample the hypothesis must be true but the conclusion is false. so if AB=5units then A could =20 units and B could =25 units. The hypothesis which is AB=5 units must stay the same, but A and B can be anything just as long as they equal 5 units.
EXCELLENT POST Rosalynn!
Nicely done – crystal clear and full of conceptual understanding!
Keep it up,
Mrs. Corricelli
for biconditionals would it be ok to think of them as biconditional = conditional + converse
Luke!
Yes; absolutely!
Nice insight,
Mrs. Corricelli
Will the biconditional statement always have a conditional and a converse? can you always find a conditional and converse in a biconditional statement? I am confused at how there can be a counterexample if it is false
Alyson,
Yes! Just like you always find two wheels on a BIcycle; there are two conditional statements (a conditional and its converse) in every biconditional!
The second question, you said you were confused at “how” there could be a counterexample. I guess I am a little confused by your question. If a conditional is false, the only way you can “prove” it is by giving a counterexample (an example where the hyp is true and the concl is false). Finding the counterexample can be a challenge. (But fun!)
Hope this helps!
Mrs. Corricelli