Question

How do you do qu2 parts a through j?

(1) Alvin, Betty, and Charlie enter a cafeteria which offers three different entrees, turkey sand- wich, veggie burger, and pizza; four different beverages, soda, water, coffee, and milk; and two types of desserts, pie and pudding. Alvin takes a turkey sandwich, a soda, and a pie. Betty takes a veggie burger, a soda, and a pie. Charlie takes a pizza and a soda. Based on this information, determine whether the following statements are true or false. (a) V people p, 3 dessert d such that p took d. (b) 3 person p such that V desserts d, p did not take d. (c) V entrees e, 3 person p such that p took e. (d) 3 entree e such that V people p, p took e. (C) V people p, p took a dessert = p did not take a pizza. (2) Which of the following are true? The domain for each is given in parentheses. (Provide a brief justification.) (a) Vc(x+1 > 1) (Real numbers) (b) 3. (2x + 3 = 5x + 1) (Natural numbers) (c) 3x(x² +1 = 2") (Real numbers) (d) 3.c (x2 = 2) (Rational numbers) (e) 3x (22 = 2) (Real numbers) (f) Vx(x + 1732 + 6x + 100 > 0) (Real numbers) (8) Vx3y(x+y=0) (Real numbers) (h) 3.Vy(x+y=0) (Real numbers) (i) Valy(y = xº) (Real numbers) 6) Valy(y = x^) (Natural numbers)

Answer 1

a) This is TRUE: as x+1 lies to the right of x by 1 unit

Vr(x +1>2)

b)
3.1 (2.c + 3 = 5x + 1)
is FALSE as
2.1 + 3 = 3T + 1 = 3T = 2 = 1 = نا | نت
(so there doesn't exists such a natural x)

c)

3.(22 +1 = 2")

For so its TRUE

r=0=2+1=1,2 = 20 = 1

d) $x^2=2\Rightarrow x=\pm \sqrt{2}$ which is irrational so this is FALSE (no rational solutions)

e) $x^2=2\Rightarrow x=\pm \sqrt{2}$ is real so this statement is TRUE

f) so this is FALSE

I= -17 + 17.02 + 60 + 100 <0

g) For every x, we can take so that this statement is TRUE

y = -2

h) This is a different statement. If x=0 then x+y=0+y=0 so y=0

And if x=1 then x+y=1+y=0 so y=-1

So there exists no such unique y meaning this statement is FALSE

i) $y=x^2$ exists and it is always unique so this statement is TRUE

j) is also a natural number so this statement is again TRUE

IEN=y= EN

$\blacksquare$

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