Question

please explain in detail the process you need to go through to get you proof by cases. Please explain in detail thank you

P, Q, R and Sare four mathematical statements such that P is a false statement and the proposition (S +Q) 4 (PAR) is a true statement. Are each of the following true, false or impossible to tell? Briefly explain all your answers with one or two brief sentences at the end. You do not need a truth table to do any of this. a) The truth value of Qis: b) The truth value of Ris: c) The truth value of Sis: Your Answer: case 1 a. The truth value of Qis false b. The truth value of Ris false c. The truth value of S is true case2 a. The truth value of Q is false b. The truth value of Ris true c. The truth value of S is true It is impossible to tell the truth value of R. The statement is only true when both are true or when both are false

Answer 1

Given, P, Q BIS 4 mathematical. statement Pis talse statement proposition (so) (PAR) is True sol & statement is only true when both are true or when both are false Rt impossible to tell the mish volue Case 1 ad-false b) R-false c) S True d) p - false st Sta (False - True false) (os a will be false as sis hue and a is false. Note (aiven statement is only true when both are true or when both are false Now PARAPS True becausp as false and R iis also tasle ssince both are mie statement ishe (so) & (PAR) – So this stament is false false. as one is false ✓ Trie

So this Care 1 implies the proposition is false when. false R is false and P is false s is true so ease 1 is not a valid because it is give that the proposition (sto) (Pag) is true But our answer contradict as we got proposition false; Now Case 9 (a) Truth value of s. is false ? (6) Truth value of R is true (Giren) Truth value of s. is time d) mith value of p is false. Note & The statement is only true when both are hue both are false. (B) (S =0) statement is false because sis mue and s is false so statement as false as one is false I (PAR) statern ent is false because p is false and R is True So, since both are hue statement is mue } or when.

(ST8) L (PAR) is true a) Truch value of 8 = false. stalemen false false As both ls+o) and (PAR) statement is false so airen station proposition is true became when both have same with value, the answer will be true, as given how So case. & is valid as it make ( S8) (PAR) a true statemeko with & fake. R Tole St True So Answer the proposition. b) Truth value of Ra Tone Truth value of Sa True. mith value of Dz false and proposition (870) E (PAR) is. True conclusion So case maker proposition IS 78.) (PAR) a mie statement a) Truth value of os e false b) mith value of Re O muth value of s d) mith value of r ž PLEASE, DO UPVOTE, CINE THUMBIS with True false UP