Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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- Please arrange in a correct order steps of the given argument in logical form. "Everyone in New Jersey lives within 50 miles of the ocean. Someone in New Jersey has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean." v (+) 3x(P(x) ^ Q(x)) Existential generalization of (%) v (%) P(c) ^ Q(c) Conjunction from ($), (&) v (&) There is x=c in the domain such that P(c) Universal instantiation (*) - (*) ♥xP(x) Hypothesis Let P(x) = "x lives within 50 miles of the ocean", and Q(x) = "x has never seen the ocean" with the domain of the variable consisting of all people who live in New Jersey. The argument in the logical form: "Everyone in New Jersey lives within 50 miles of the ocean"= VxP(x) "Someone in New Jersey has never seen the ocean" = 3xQ(x) Someone who lives within 50 miles of the ocean has never seen the ocean =3(P(x) ^ Q(x))arrow_forwardpls answerarrow_forward1 Vx2 + 1 x2V x² +1 True Falsearrow_forward
- In WA, you can enter sec2(x) either by typing sec²(x), (sec(x))², or sec(x)2. Therefore, be aware of the difference between sec(x?) and sec(x)2. We must remember this syntax for this course. (a) Enter sec2(x). (b) Enter sec(x?). (c) sec2(x) Select your answer sec(x2). (d) sec2(x) Select your answer sec(x)².arrow_forwardLet C(x) be the predicate " is a comedian", and let F(x) be the predicate" is funny." Match the statements below on the left to their equivalent English translations on the right. DOD Vx(F(x) ^ C(x)) Vx (F(x) → C(x)) 3x(F(x) V-C(x)) Vx-(F(x) ^ C'(x)) 3x (F(x)^-C(x)) Vx (C(x)→-F(x)) 1. All funny people are comedians. Not all funny people are comedians. 2. 3. No comedian is funny. 4. Everyone is a funny comedian. It is not the case that everyone is a funny comedian. 6. No one is a funny comedian. 5.arrow_forward
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