This preview shows pages 1–2. Sign up to view the full content.
Solutions to Problems on Implication
Problem 1:
A mother and her son were in the New River Valley Mall. The son was begging for Ice
Cream. The mother said to her son,
“
If you do not behave, I will not buy you any ice cream
!”
Let B be the statement “Behave” and I be the statement “buy ice cream”
Then we have
B
II B
→≡
→
∼∼
where I is sufficient condition and B is the
necessary. (It is usually easier to represent statements as positive)
A)
Which of the following statements are equivalent to the mother’s statement to
her son?
Justify your answer.
1)
Behave or no ice cream.
Ans:
B
II
B
I
B
∨≡
∨
≡
→
and the sufficient and necessary condition match with
the original statement.
2)
You must behave before I will buy you any ice cream.
Ans:
The word “must”
means that B is a necessary condition and I is the sufficient
condition which match with the original statement.
3)
Your good behavior guarantees some ice cream.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 MPMcQuain
 Math

Click to edit the document details