Suppose each of the following three statements is true:John is smart.John or Mary is ten years old.If Mary is ten years old, then John is not smart.Which of the following is true and why?a.) Mary is 10 years old.b.) John is 10 years old.c.) Either John or Mary is not 10 years old.

Question
Asked Jan 24, 2019
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Suppose each of the following three statements is true:
John is smart.
John or Mary is ten years old.
If Mary is ten years old, then John is not smart.
Which of the following is true and why?
a.) Mary is 10 years old.
b.) John is 10 years old.
c.) Either John or Mary is not 10 years old.

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Expert Answer

Step 1

To find which of the statements is true and why if the three statements are true:

John is smart.
John or Mary is ten years old.
If Mary is ten years old, then John is not smart.

a.) Mary is 10 years old.
b.) John is 10 years old.
c.) Either John or Mary is not 10 years old.

So, the correct option is b and c which is true

Step 2

In “a” option it is stated that “Mary is 10 years old” which is not true because according to the given statements which are true john is smart so Mary cannot be 10 years old. If Mary would be 10 years old John would not be smart.

Step 3

In “b” option it is stated that “John is 10 years old” which is true because according to the given statements...

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