Arguments/Logical Thinking - English to Math

Formulate the arguments below symbolically and
determine whether each is valid with reasons.

Let p: I study hard.     g: I get A’s.      r: I get rich.

1. English	Math
   If I study hard, then I get A's. I study hard. ∴ I get A's.

   Is it valid? _________
   Why?

2. English	Math
   If I study hard or I get rich, then I get A's. I get A's ∴ If I don't study hard, then I get rich.

   Is it valid? _________
   Why?

3. English	Math
   If I study hard, then I get A's or I get rich. I don't get A's and I don’t get rich. ∴ If I don’t study hard, then I get rich.

   Is it valid? _________
   Why?

Arguments/Logical Thinking - Math to English

Write the given argument in words and
determine whether each argument is valid with reasons.

Let p: 4 megabytes is better than no memory at all.
    q: We will buy more memory
    r: We will buy a new computer.

4. Math	English
   p ⟶ r p ⟶ q ∴ p ⟶ (r ∧ q)

   Is it valid? _________
   Why?

5. Math	English
   ∼r ⟶ ∼p r ∴ p

   Is it valid? _________
   Why?

Valid or Invalid Decision

	6. Reason:
	7. Reason:
	8. Reason:
	9. Reason:
	10. Reason: