Wednesday

March 4, 2015

March 4, 2015

Posted by **Jen** on Friday, July 15, 2011 at 11:12am.

I) If the garden needs watering, then the garden does not need weeding.

II) Either the garden needs watering or the garden does not need weeding.

III) If the garden does not need watering, then the garden does not need weeding.

a. None are equivalent

b. I, II, and III are equivalent

c. I and II are equivalent

d. I and III are equivalent

e. II and III are equivalent

- Math -
**Ms. Sue**, Friday, July 15, 2011 at 11:40amI'll be glad to comment on your answer.

- Math -
**Jen**, Friday, July 15, 2011 at 11:44amI think it's b. but i'm not sure what my reasoning would be....

- Math -
**Ms. Sue**, Friday, July 15, 2011 at 11:48amI disagree with your answer.

I. states that if the garden is dry, the weeds don't grow.

II. states an either/or situation -- either it's dry or the weeds don't grow.

III. states that if it's wet, then the weeds don't grow.

- Math -
**Max**, Friday, July 15, 2011 at 12:46pmDisregard my previous post on a similar question. I now have a better understanding.

I suggest converting each statement into symbolic form.

Let p = the garden needs watering.

Let p = the garden needs weeding.

I. p --> ~q

II. p V ~q

III. ~p --> q

Looks like the answer is a; none of them are equivalent.

Here's a side note: a statement is always logically equivalent to it's contrapositive, i.e., p --> q is equivalent to ~q --> ~p.

If I am in Paris, then I am in France.

If I am not in France, then I am not in Paris.

II.

**Answer this Question**

**Related Questions**

Math - The dimensions of Mrs. Singleton's square garden are dilated using a ...

Math - Marisa spent 5 hours watering her garden by hand. She spent the same ...

Maath:) - Sam is going to plant a rectangular flower garden next to his house. ...

Math - Mr Townes created a 2foot wide garden path around a circular garden. The ...

math - a worker in a city park needs to cover a circular path around the outside...

Math - Mr. Brown needs to buy some fencing for his garden (too many rabbits have...

math - John wants to put a circular garden in his back yard. The garden has a ...

math - John wants to put a circular garden in his back yard. The garden has a ...

math - a farmer needs to buy fencing to go around his garden. The garden is a 20...

algebra 1 - Charles wants to build a vegetable garden such that three sides of ...