Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. 1)  recall, a truth table for a proposition

1)  Recall, a truth table for a proposition involving propositional symbols p and q uses four rows...

50.1K

Verified Solution

Question

Advance Math

1)  Recall, a truth table for a proposition involvingpropositional symbols p and q uses four rows for the cases p true,q true, p true, q false, p false, q true and p false, q false (inthat order). For example  the outcome for p v¬q  is  T, T, F, T  since theexpression is only false when q is true but p is false. Of course,we have the same outcome for any logically equivalent propositionincluding ¬(¬p ∧ q), (¬p ∧ q) → false  and q → p. Ofthese, q → p clearly reduces the number of symbols to a bareminimum. Find \"minimal expressions\" for the other 15 possibleoutcomes, which are listed below:

a) FFFF

b) FFFT

c) FFTF

d) FFTT

e) FTFF

f) FTFT

g) FTTF

h) FTTT

i) TFFF

j) TFFT

k) TFTF

l) TFTT

m) TTFF

n) TTTF

o) TTTT

You may only use symbols from the set p, q, → , ∧ , ∨,(,  ),  ↔ ,false,  true, ¬ .  Each ofthose count 1 toward the length of the expression.(Note:  falseand true still count assingle symbols, even though they have multiple letters.) In some ofthe answers, your expression might have just p in it and not q orvice versa. Of course, there are also two answers that don't haveeither p or q in them!

Answer & Explanation Solved by verified expert
4.2 Ratings (581 Votes)
page    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Advance Math
1.2K views

. Let x, y ? R {0}. Prove that if x < x^(?1) <...

Physics
1.2K views

A plane progressive sound wave of frequency 160 Hz is moving along vector 31 4j...

Geometry
1.2K views

A solid oblique cone with a slant length of 17 units is placed inside an...

Basic Math
1.2K views

The equations of two conics are given below Choose the correct classification for each and...

Statistics
1.2K views

You conduct a simulation regarding how many registered voters voted in the last election Your...

Accounting
1.2K views

Perpetual inventory using LIFO Beginning inventory, purchases, and sales for Item 88-HX are as...

Accounting
1.2K views

Interest expenses OMR 200 Interest payable OMR 100 Advertisement OMR 50 Insurance expense OMR 60...

Accounting
1.2K views

Minnesota Mining paid $600,000 to obtain the rights to mine on a piece of land....

Accounting
1.2K views

At the end of the year, before distributions, Bombay (an S corporation) has an accumulated...

Accounting
1.2K views

21.1 A resident company pays a fully franked dividend of $700 to a resident shareholder....

Finance
1.2K views

anyone can write me a report about financial decicions about 5 rounds in capsim?

Finance
1.2K views

Answer 5-10 Present Value of an Annuity Finding the present value of an annuity...