I-B. Show that the following are tautologies.a) (р ^а) — рb) р — (pVq)c) ((p → q) ^ (q → r)) → (p → r)d) ((p V q) ^ (~p)) → qe) ((p → r) ^ (q →r)) → ((p V q) →r)

Answered: Image /qna-images/answer/61392dfb-decb-4e84-8a35-e640a7015542.jpg

Answered: I-B. Show that the following are…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. For the following, show that KB does not entail a: a) KB = {(pVr) =¬q,¬r= q}; a = (p=r) b) KB = {p →q, ~(s^p)}; a= (sa q)
C Clever | Portal 1 of 3 7) -3-4sec 0 = V2 - 3-3sec 0 7n 5T A) { 6. 5n 7t B) {- 4. 6. 6. T 7n C) 3n 5n D) 4 4 4
36²) For A = [0, to, 1} & B = {₁, ₂} & universum U = {0, +, 1, 0₁7, 23 Find: A, B, AUB, AnB, A¹B, BA, A ₂B, 3(A)=2A, AXB & BXA. (i) Similarly for A={(x,y): x = 1 z & B=√(x, y): y = xy & U = IR*IR=1R² find AUB, AB, BA, A' & B! AnB
(p→9）A（g→r） a) tautologies c) contraction b) not one of the previous answers
Given A-() . :). 2 3 and B 2 -1 Select the option(s) below which represent (АВ ") 1. B-'A-1. BA-!. :). 3.5 2.5 1.5 0.5 A-'B. :)- -3.5 -2.5 -1.5 -0.5
Let T (c, d) mean “c is taller than d,” G(c) mean “c is a giraffe,” N (c)mean “c is a gnu,” L(c) mean “c is a lion, and Z(c) mean “c is a zebra.Then from the axioms(I) (∀c)(∀d)(G(c) →(N (d) →T (c, d))) (every giraffe is taller than everygnu),(II) (∃c)(N (c)∧(∀d)(L(d) →T (c, d))) (some gnu is taller than every lion),and(III) (∃c, d)(L(c) ∧Z(d) ∧T (c, d)) (some lion is taller than some zebra),1prove that every giraffe is taller than some zebra, i.e.,(∀c)(G(c) →(∃d)(Z(d) ∧T (c, d))).
Exauple: If v=(T') is a contravarient vetor, Shew that He Parhil cderivatones %3D de fined in each ceordinede 〒-TYえ x るx x) System, transform allrding to the rule さえ Sざa るえ

urgent
Rewrite the following compound propositions to associate the correct order of connectives on the following by putting a parenthesis, a bracket, or a brace. . 1. p → qv ~r 2. p→- q→ r^~s 3. - pnqvr s→~q 4. - p>q →~rVs>~(s^t) 5. (p → q) ^(r –→ s) → pvr → q v s
The G.S for axðy is اختر احدي الدبابات z=Cfy+ 2x) + czf(y 3x) a. z= Cfy+2x) + czf(y -x) b. z=Gf&+ 2x) + CzxfO + 2x) z=cfy+2x) + C2f(y + 3x) d.
Explain the determine red and the eqautions are here

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I-B. Show that the following are tautologies. a) (р ^а) — р b) р — (рVq) c) ((p → q) ^ (q → r)) → (p → r) d) ((pvq)л(~р)) — q e) ((p → r) A (q →r)) → ((p V q) → r)