Question

Give direct and indirect proofs of: (a) a → b, c → b, d → (a...

Give direct and indirect proofs of:

(a) a → b, c → b, d → (a ∨ c), d ⇒ b.

(b) (p → q) ∧ (r → s),(q → t) ∧ (s → u), ¬(t ∧ u), p → r ⇒ ¬p.

(c) p → (q → r), ¬s\/p, q ⇒ s → r.

(d) p → q, q → r, ¬(p ∧ r), p ∨ r ⇒ r.

(e) ¬q, p → q, p ∨ t ⇒ t

Please explain if possible. I don't understand how to set up like what is considered premise and when (or which) law to apply. Thanks!

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

18 Rules of Inference/Replacement for Propositional Logic is usused. I have solved only first four parts.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Give direct and indirect proofs of: a. p → (q → r), ¬s ∨ p, q...
Give direct and indirect proofs of: a. p → (q → r), ¬s ∨ p, q ⇒ s → r. b. p → q, q → r, ¬(p ∧ r), p ∨ r ⇒ r
Give the indirect proofs of: p→q,¬r→¬q,¬r⇒¬p.p→q,¬r→¬q,¬r⇒¬p. p→¬q,¬r→q,p⇒r.p→¬q,¬r→q,p⇒r. a∨b,c∧d,a→¬c⇒b.
Give the indirect proofs of: p→q,¬r→¬q,¬r⇒¬p.p→q,¬r→¬q,¬r⇒¬p. p→¬q,¬r→q,p⇒r.p→¬q,¬r→q,p⇒r. a∨b,c∧d,a→¬c⇒b.
A subset of a power set. (a) Let X = {a, b, c, d}. What is...
A subset of a power set. (a) Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }? comment: Please give a clear explanation to what this set builder notation translate to? Because I've checked the answer for a) and it is A= {{a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}}. I don't understand because the cardinality of A has to be 2 right? Meanwhile, the answer is basically saying there's 6 elements. So...
Give both a direct proof and an indirect proof of the statement, “If A ⊆ B,...
Give both a direct proof and an indirect proof of the statement, “If A ⊆ B, then A\(B\C) ⊆ C.” [Both Show-lines and a final presentation are required.]
4. Consider the relation schema R(ABCDE) with the set of functional dependencies F={B→E, A→B, DE→C, D→A,...
4. Consider the relation schema R(ABCDE) with the set of functional dependencies F={B→E, A→B, DE→C, D→A, C→AE}. For the following relations resulting from a possible decomposition of R, identify the non-trivial functional dependencies which can be projected to each of the decomposed relations. a) S(ABC) b) T(BCE) c) U(ABDE
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...
All of the following anions are considered basic except A) F-. B) CN-. C) PO43-. D)...
All of the following anions are considered basic except A) F-. B) CN-. C) PO43-. D) HPO42-. E) Cl-. Apparently the answer is E) Cl- but I dont understand, if Cl- is not basic than why isn't F- not also basic? Even with the differences in electronegativity I don't understand. Thanks for ypur help!
Prove or give a counter-example: (a) if R ⊂ S and T ⊂ U then T\...
Prove or give a counter-example: (a) if R ⊂ S and T ⊂ U then T\ S ⊂ U \R. (b) if R∪S⊂T∪U, R∩S= Ø and T⊂ R, then S ⊂ U. (c) if R ∩ S⊂T ∩ S then R⊂T. (d) R\ (S\T)=(R\S) \ T
Please quesiton on database function dependency: Suppose we have relation R (A, B, C, D, E),...
Please quesiton on database function dependency: Suppose we have relation R (A, B, C, D, E), with some set of FD’s , and we wish to project those FD’s onto relation S (A, B, C). Give the FD’s that hold in S if the FD’s for R are: c) AB --> D, AC --> E, BC --> D, D --> A, and E --> B. d) A --> B, B --> C, C --> D, D --> E, and E...
which of the following is a theory of copyright infringement? a- vicarious b- direct c- indirect...
which of the following is a theory of copyright infringement? a- vicarious b- direct c- indirect d- all of the above
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT