Problem 1. The purpose of this problem is to practice the use of logic operations and...

Problem 1. The purpose of this problem is to practice the use of logic operations and quantifiers. For each Statement X below determine if each of the three statementsX1, X2, X3 that follow it satisfy the following:

a) Xi implies X;
b) X implies Xi;
c) if Xi is true then X must be false; d) if X is true then Xi must be false.

Statement A. In every house there is a mouse.

A1. There is no house without a mouse.A2. There exists a house without a mouse.A3. Mice don’t live in houses.

Statement B. For every mouse there is a blouse, such that if the mouse wears the blouse he’ll get a gift from Carl Friedrich Gauss.

B1. There is a mouse that can wear any blouse, but still won’t get a gift from Gauss.

B2. There are no mice for which there does not exist a special blouse, such that if the mouse is not getting a gift from Gauss it means that he did not wear that blouse.B3. If a mouse did not get a gift from Gauss, it must be that he hasn’t tried on all

the blouses yet.
Statement C. If Statement A is true then Statement B is true.

C1. In every house there is a mouse that never wore a blouse, but got a gift from Gauss.

C2. Every house has at least 3 mice, but under no condition would Gauss give something to a mouse.

C3. There is a mouse in my house that likes to wear a silver blouse and got some cookies from my spouse. (My name’s Johanna Gauss).

Expert Solution

milcah answered 1 year ago

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