The statement \"If it\'s a dog, then it is a mammal\" may be rephrased as which

Question

The statement "If it's a dog, then it is a mammal" may be rephrased as which of the following? Explain your reasoning.

A. All mammals are dogs. A common alternative way of stating "if p, then q" is "all q are p."

b.Being a mammal is necessary for being a dog. A common alternative way of stating "if p, then q" is "q is necessary for p

c.Being a mammal is sufficient for being a dog. The only alternative way of stating "if p, then q" is "q is sufficient for p."

d.Being a mammal is sufficient for being a dog. A common alternative way of stating "if p, then q" is "q is sufficient for p."

e.Being a mammal is necessary for being a dog. The only alternative way of stating "if p, then q" is "q is necessary for p."

f.All mammals are dogs. The only alternative way of stating "if p, then q" is "all q are p."

( what would be the right answer)

Explanation / Answer

Solution: The correct option is B) Being a mammal is necessary for being a dog. A common alternative way of stating "if p, then q" is "q is necessary for p".

We are given the conditional statement that ""If it's a dog, then it is a mammal". The alternative ways to rephrase a condition statement of "If p, then q" are as follows:

1) p is sufficient for q.

2) p will lead to q

3) p implies q.

4) q is necessary for p.

5) q if p.

6) q whenever p

Hence, only B) is correct.

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