Use the Law of Syllogism and the Law of Detachment to make conclusions between the statements A, D, and E.
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 the conclusion of Statement A matches the hypothesis of Statement D, let's use the Law of Syllogism to make our first conclusion.
If p → q &is true
and q → r &is true,
then p → r &is true.
Applying the Law of Syllogism, we can make a valid conclusion.
Conclusion I
If Maria is drinking juice,
then then Julio is drinking juice and nothing else.
Next, when we compare Conclusion I and Statement E, we see that Statement E matches the hypothesis of Conclusion I. Thus, we can use the Law of Detachment to make a second conclusion between Statement E and Conclusion I.
If p → r &is true
and p &is true,
then r &is true.
Having used the Law of Detachment, we have the second conclusion.
Conclusion II
Julio is drinking juice and nothing else.
Now, we are ready to determine the truth value of the statement given below.
Statement
Julio is drinking juice.
Looking at Conclusion II that we made, we can say that the given statement must be true.
