Question
Consider the following argument. Premise: If a food is an apple, then it is a fruit. Premise: A dog is not a fruit. Conclusion: A dog is not a type of apple. a. Identify the form of the conditional argument and determine its validity with a Venn diagram. b. Evaluate the truth of the premises and state whether the argument is sound. a. The argument is square square affirming the conclusion. affirming the hypothesis. denying the conclusion.
Answer
4.1
(330 Votes)
Megan
Elite · Tutor for 8 years
Answer
a. The form of the conditional argument is denying the hypothesis. To determine its validity with a Venn diagram:- Let's represent the set of apples as circle A (since the first premise states, "If a food is an apple, then it is a fruit").- Let's represent the set of fruits as the larger set B.Now, we can visually represent the argument:1. Shade the portion of circle A that does not overlap with circle B to represent "a food is an apple."2. Place a point in the shaded area to represent "a food is an apple, then it is a fruit."3. Since the second premise is "dog is not a fruit," place a point outside the region covered by circle B.Now, observe that there is no overlap between the region representing apples (circle A) and the region outside the region representing fruits. This aligns with the conclusion that "A dog is not a type of apple." Therefore, the argument is valid.b. The truth of the premises:- The first premise is generally true: If something is an apple, it is indeed a type of fruit.- The second premise is also true: A dog is not a type of fruit.Since both premises are true and the argument is valid, it is sound.