logic questions.?

Question

Given that:

If I buy a shirt, then I will buy a vest.
If I do not have any money, then I will not buy a vest.
Either I buy a shirt or I will not go to the dance.
I am going to the dance.
Do I have any money?

1. yes
2. no
3. cannot tell
--
and

Given the statement: "If two sides of a triangle are congruent, then the angles opposite these sides are congruent."
Given the converse of the statement: "If two angles of a triangle are congruent, then the sides opposite these angles are congruent."
What is true about this statement and its converse?

1. Both the statement and its converse are true.
2. Neither the statement nor its converse is true.
3. The statement is true but its converse is false.
4. The statement is false but its converse is true.

Answer 1

"Either I buy a shirt or I will not go to the dance" means:
'If I buy a shirt, i'll go to the dance' AND 'If I don't have a shirt. then I don't go to the dance'.
The Contrapositive of that last statement is:
If I go to the dance, I buy a shirt.
You go to the dance, thus you have a shirt.
Thus, you'll buy a vest (top statement).
Contrapositive of second statment:
If i DO buy a vest, then I DO have money.
You buy a vest, so you have money. QED.
1, YES.

and for the second one:
1, both.

Answer 2

You are going to the dance, so you are buying a shirt.
Since you bought a shirt, you will buy a vest.
And that means you do have money, or you will not buy a vest.
1. yes

1. Both the statement and its converse are true.



EDIT ::

Ranto is aging with his many years of training and got his logic all messed up and wrong.


Consider the following statement:

. . . Either A or B

It is true if :

A = true, B = true
A = true, B = false
A = false, B = true

It is false if
A = false, B = false

B says I will NOT go to the dance.
So B is false, and therefore A = true
And therefore you bought a shirt, and yes, you have money.

Answer 3

For the first one -- you cannot tell.

The mistake that everyone else is making is that they think that they can tell whether or not you buy a shirt.

Consider the following statement:

. . . Either I buy a shirt or I will not go to the dance.

It is true if :

You do not buy a shirt and do go to the dance
You buy a shirt and do not go to the dance
You buy a shirt and do go to the dance.

Iit is only false if you do not go to the dance and do not buy a shirt.

Knowing that you went to the dance does not give us any information about whether or not you bought the shirt. We can infer that you need money to buy the shirt -- but not that you bought one.

We are not told that you need money to dance.

The answer to the other problem is Both.

Answer 4

First one is Cannot Tell because it says he/she is going to the dance which requires you to buy a shirt which requires you to buy a vest. And it says that if you donnot have money you will buy a vest, which might have been the case, however, it doesn't say that if you have money you will not buy it, therefore you cannot tell.

Second one is Both the statement and it's converse are true. No explaining needed.


TRUST ME IT IS CANNOT TELL, READ MY EXPLANATION

Answer 5

Yes, if you're going to the dance, you have money.