Use the Law of Detachment to make a conclusion between the statements A, and E. Then use Statement C to determine the truth value of the given statement. Notice that breakfast time is also mealtime.
Truth Value:must be true Explanation: See solution.
Practice makes perfect
The following statements are given and we will assume that they are true.
A. If Maria is drinking juice, then it is breakfast time.
B. If it if lunchtime, then Kira is drinking milk and nothing else.
C. If it is mealtime, then Curtis is drinking water and nothing else.
D. If it is breakfast time, then Julio is drinking juice and nothing else.
E. Maria is drinking juice.
Let's make some conclusions to determine the truth value of the given statement. Since Statement E matches the hypothesis of Statement A, let's use the Law of Detachment to make a conclusion between Statement E and Statement A.
If p → q &is true
and p &is true,
then q &is true.
Having used the Law of Detachment, we make a valid conclusion.
Conclusion I
It is breakfast time.
Notice that breakfast time is also mealtime. Thus, Conclusion I matches the hypothesis of Statement C. In this case, we will use the Law of Detachment one more time to make a final conclusion.
Conclusion II
Curtis is drinking water and nothing else.
Now, we are ready to determine the truth value of the statement given below.
Statement
Curtis is drinking water.
As a result, we can say that the given Statement must be true based on Conclusion II.
