Question

check your understanding
at the two sentences below.
if something has stripes, then it is a zebra.
if something is a zebra, then it has stripes.
which of the two sentences, if any, is true? how do you know?
decide whether the statement is true or false. if false, give a counterexample.
a. if i have 25 cents, then i have 2 dimes and a nickel.
b. if a number is divisible by 4, then that number is divisible by 2.
c. if a figure is a rectangle, then it has 4 sides.

1. consider the statement: if your body temperature is 103°, then you have a fever.

Explanation:

Step1: Analyze "If something has stripes, then it is a zebra"

This statement is false. Counter - example: A tiger has stripes but is not a zebra.

Step2: Analyze "If something is a zebra, then it has stripes"

This statement is true as having stripes is a characteristic of zebras.

Step3: Analyze "If I have 25 cents, then I have 2 dimes and a nickel"

This statement is false. Counter - example: I could have 1 quarter (which is also 25 cents).

Step4: Analyze "If a number is divisible by 4, then that number is divisible by 2"

This statement is true. Since 4 = 2×2, any number divisible by 4 can be written as 4k (k is an integer), and 4k=2×(2k), so it is divisible by 2.

Step5: Analyze "If a figure is a rectangle, then it has 4 sides"

This statement is true. By the definition of a rectangle, it is a four - sided polygon.

Step6: Analyze "If your body temperature is 103°, then you have a fever"

The condition is "your body temperature is 103°" and the conclusion is "you have a fever".

Answer:

1. "If something has stripes, then it is a zebra" is false (counter - example: tiger). "If something is a zebra, then it has stripes" is true.
2. a. False (counter - example: 1 quarter). b. True. c. True.
3. Condition: your body temperature is 103°. Conclusion: you have a fever.