Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
2. Inductive and Deductive Reasoning
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Exercise 45 Page 82

Practice makes perfect
a Let's highlight the statements we need.
  • Yellowstone is a national park in Wyoming.
  • You and your friend went camping at Yellowstone National Park.
  • When you go camping, you go canoeing.
  • If you go on a hike, your friend goes with you.
  • You go on a hike.
  • There is a 3-mile-long trail near your campsite.

Since Yellowstone is a park in Wyoming, and you went camping at Yellowstone, we can conclude that this is a valid statement.

b Let's highlight the statements we need.
  • Yellowstone is a national park in Wyoming.
  • You and your friend went camping at Yellowstone National Park.
  • When you go camping, you go canoeing.
  • If you go on a hike, your friend goes with you.
  • You go on a hike.
  • There is a 3-mile-long trail near your campsite.

Notice that the statement only says that you go camping. It does not say anything about your friend tagging along. Therefore, we cannot conclude that this statement is valid.

c Let's highlight the statements we need.
  • Yellowstone is a national park in Wyoming.
  • You and your friend went camping at Yellowstone National Park.
  • When you go camping, you go canoeing.
  • If you go on a hike, your friend goes with you.
  • You go on a hike.
  • There is a 3-mile-long trail near your campsite.

Since the fourth statement says that your friend goes with you when you go on a hike, and we know you go on a hike, we can conclude this statement as valid

d We already know from Part C that you and your friend went on a hike. However, there is no information stating how long that hike was. Even though there is a 3 mile long trail near your campsite, it does not mean that you took that trail.