Question

assume that the set of given information is true. use the law of syllogism to write a conditional.
if a baby is feeling nauseous, then the baby is ill.
if a baby is ill, then the baby must be brought to the physician’s office.

choose the correct conditional below

a. if a baby is brought to the physician’s office, then the baby must be feeling nauseous.

b. if a baby is not brought to the physician’s office, then the baby is not ill.

c. if a baby is feeling nauseous, then the baby is not ill.

d. if a baby is not ill, then the baby is not feeling nauseous.

e. if a baby is brought to the physician’s office, then the baby is ill.

f. if a baby is not feeling nauseous, then the baby is not ill.

g. if a baby is feeling nauseous, then the baby must be brought to the physician’s office.

help me solve this

Explanation:

Step1: Recall the Law of Syllogism

The Law of Syllogism states that if we have two conditionals \( p \to q \) and \( q \to r \), then we can conclude \( p \to r \).

Let \( p \): "a baby is feeling nauseous", \( q \): "the baby is ill", \( r \): "the baby must be brought to the physician’s office".

The first conditional is \( p \to q \) (If a baby is feeling nauseous, then the baby is ill), and the second is \( q \to r \) (If a baby is ill, then the baby must be brought to the physician’s office).

Step2: Apply the Law of Syllogism

Using the Law of Syllogism, we combine \( p \to q \) and \( q \to r \) to get \( p \to r \). Translating back, this means "If a baby is feeling nauseous, then the baby must be brought to the physician’s office".

Now let's analyze each option:

• Option A: This is \( r \to p \), which is not a valid conclusion from the given conditionals (affirming the consequent).
• Option B: This is \(

eg r \to
eg q \), which is the contrapositive of \( q \to r \), but not the conclusion from the Law of Syllogism.

• Option C: This contradicts the first conditional \( p \to q \).
• Option D: This is the contrapositive of \( p \to q \) ( \(

eg q \to
eg p \) ), not the syllogism conclusion.

• Option E: This is \( r \to q \), which is not a valid conclusion (affirming the consequent of \( q \to r \)).
• Option F: This is \(

eg p \to
eg q \), which is not a valid conclusion from the syllogism.

• Option G: This is \( p \to r \), which matches the conclusion from the Law of Syllogism.

Answer:

G. If a baby is feeling nauseous, then the baby must be brought to the physician's office.