MATH 220 Midterm: MATH 220 TAMU 220-Fall 03 Exam 1Solutions

27 views2 pages

turquoisegnu128

31 Jan 2019

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

4 ; 1: there are several ways to do this problem, either by manipulating the logical symbols algebraically or by writing out the truth tables. Or by a combination of both. (a) the truth table for p (p q): P q p q p (p q) Since p (p q) has the same truth values as p q, they are equivalent. So the answer is (j). (b) we simplify a little bit: equivalent to p q by de morgan"s laws. 6= q p is equivalent to q p , and (p q) is. P q q p p q ( q p ) ( (p q)) This matches up with p , so the answer is (i). (c) we convert the implications to or statements: so ((p q) q) p is equivalent to. ( (p q) q) p. ( ( p q) q) p, which we can simplify using de morgan"s laws to (( p q) q) p.

Related Questions

please show all steps.

Show transcribed image text

magentaraccoon707

[1] 1. (a) Solve 2 – 31 < 7. Solution: We have – 7<-3 < 7 which gives -4 0 on (-0, 1] U [2,). Next, we need to see where Vr2 – 3r +2 -1 > 0. If r2 - 3.c + 2 – 1 > 0, then V.22 – 3.0 +2 > . Observe that this is definitely true if r < 0. If r > 0, then squar- ing both sides we get 22 - 3.+2 > 1 2 > 3. V A VICO Thus, the domain of f is (-00, ). [2] (c) Find the exact value of tan(sec-14). Solution: Let y = sec-14. Then, sec y = 4. From the diagram we get that tan(sec-? 4) = tan y = 15 [2] (d) Find all r such that sin(2.x) = COS I. Solution: We have 2 sin r cos r = COS I, SO 0 = 2 sin Cos I -Cos I = cos .r (2 sin c - 1). Hence, sin(2x) = cost when cos x = 0, or when sin r = Thus, r= +ik, kez, I= +2nk, ke Z, or r= +2nk, kez [2] (e) State the precise mathematical definition of lim f(x) = 0. Solution: For every e > 0 there exists a 8 >0 such that if 0 < x-al <, then f(c) >

Show transcribed image text

greyplatypus986

MATH 220 Midterm: MATH 220 TAMU 220-Fall 03 Exam 1Solutions

Document Summary

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH 220 Midterm: MATH 220 TAMU 220-Fall 03 Exam 2

MATH 220 Midterm: MATH 220 TAMU 220-Fall 03 Exam 1

MATH 220 Midterm: MATH 220 TAMU 220-Fall 03 Exam 2Solutions

Related Questions