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Convert the following statement using an "if-then" structure.

John doesn't own a dog, or he owns a cat.John doesn't own a dog, or he owns a cat.

Choose the correct statement:
A. If John doesn't own a cat, then he owns a dog
B. If John owns a cat, then he owns a dog
C. If John doesn't own a dog, then he owns a cat
D. If John owns a dog, then he owns a cat

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sqdancefan

Answer:

  D. If John owns a dog, then he owns a cat

Step-by-step explanation:

The implication p → q (if p, then q) has the same truth table as the logical expression ~p∨q. You have the expression ...

  ~(John owns a dog) ∨ (he owns a cat)

Matching parts of this expression to the components of the expression ~p∨q, we see we can choose ...

  • p = John owns a dog
  • q = he owns a cat

and put those into the structure of the implication: if p, then q.

  If John owns a dog, then he owns a cat. . . . . matches choice D

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