Question

The temperature is not 90° if and only if the air conditioner is not working, or the apartment is not hot.

Answer 1

here is what i did for it if some one can look it over for me it seem that im missing something in it

Answer 2

X = temperature of 90 degrees

C = air conditioner working

H = apartment hot

"OR" =(written as v)a logical operation in which either or both input values produce a "true" result

"NOT" = (written as ~) a negation

"Conditional If-Then" = (written as →) If the statement preceding this symbol is true, then the statement following this statement is also true.

"if and only if" = (written as ↔) biconditional

"T" = True

"F" = False

The purpose of logic is to enable me to construct valid arguments which satisfy my basic premise: "If all of my premises are true, then my conclusion must also be true."

My original problem statement is: The temperature is not 90 degrees if and only if the air conditioner is not working or the apartment is not hot.

It will be helpful to rewrite the problem statement as follows:

If and only if the Air Conditioner is not working or the apartment is not hot, then the temperature is not 90 degrees.

The Boolean expression for this statement can be written:

(~C v ~H) ↔~X

This relationship can be also expressed in a "Truth Table".

A truth table is a list of every possible combination of input values and the output value for each combination. It is a picture of every possibility.

A "Truth Table" for my problem statement looks like this:

Truth Table

C H X (~C v ~H) ↔~X

T T T T


T T F F

T F T F

T F F T

F T T F

F T F T

F F T F

F F F T