Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Turner

Read the two statements shown below. If the weather is not cold, Meg will go swimming. The weather is cold, or Meg will go swimming. Create truth tables for the logical form of the two statements (not to be submitted). Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.

  • one year ago
  • one year ago

  • This Question is Closed
  1. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    they are equivalent, as the truth tables are the same to turn \(P\to Q\) into an equivalent or statement \[P\to Q\equiv \lnot P\lor Q\]

    • one year ago
  2. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    here is the truth table for \(P\to Q\) \[\begin{array}{|c|c|c} P & Q & P\to{}Q \\ \hline T & T &T \\ T & F & F \\ F & T & T \\ F & F & T \\ \hline \end{array}\]

    • one year ago
  3. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    and here it is for \(\lnot P\lor Q\) \[\begin{array}{|c|c|c|c} P & Q & \lnot{}P & \lnot{}P\lor{}Q \\ \hline T & T & F & T \\ T & F & F & F \\ F & T & T & T \\ F & F & T & T \\ \hline \end{array}\]

    • one year ago
  4. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    you can see that the last columns are identical, so it is equivalent

    • one year ago
  5. Turner
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks you so much!! So if I wrote this in sentence form would this be correct These statements are equivalent, as their truth tables are the same. The P is true twice, and false twice for both statements, then the Q is T then F then T then F for both statements. The truth table column for P→Q is T, F, T, T as it is the same for ¬P∨Q.

    • one year ago
  6. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    yes although i would skip " The P is true twice, and false twice for both statements, then the Q is T then F then T then F for both statements." that is just how the truth table is constructed maybe put

    • one year ago
  7. Turner
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.