# Truth tables and logic statements

1. Write a truth table to determine whether the two statements are equivalent and explain your answer.

~(q-->P) v r , (p v q) --> ~r

2. Write a negation of the following statement and explain your answer.

Some diet sodas contain saccharin.

3. Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion and explain your work.

I) If the house is not white, then the house is not small.

II) The house is not white and the house is small.

III) It is false that the house is white or that the house is not small.

4. Write the compound statement in symbols.

Let R = The food is good, P = I eat too much, Q = I'll exercise.

If I exercise, then the food won't be good and I won't eat too much.

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#### Solution Preview

1. Start by writing truth values for P, Q, and R in every possible combination. It will look just like this:

P Q R

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

Next, make columns for each piece, one at a time, and find truth values by comparing the previous columns. Work inside parentheses first, just like the order of operations.

P Q R (Q --> P) ~(Q --> P) ~(Q --> P) v R (P v Q) ~R (p v q) --> ~R

T T T T ...

#### Solution Summary

Truth tables and logic statements are shown in appropriate symbols.