CISC 102 Lecture 4: Laws of Set Theory

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chocolatemink31

17 Oct 2016

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A a = a (a b) c = a (b c) A (b c) = (a b) (a c) You can verify these properties with u = {1, 2, 3, 4, 5, 6, 7), a= {1, 2, 3}, You can verify these properties with u = {1, 2, 3, 4, 5, 5, 6}, a = {1, 2, 3}, b = {2, 4, 5} Definition: a set is said to be finite if s is empty or if s contains exactly m elements where m is a positive integer, otherwise s is infinite. We use (cid:448)erti(cid:272)al (cid:271)ars (cid:862)||(cid:863)to de(cid:374)ote the size or (cid:272)ardi(cid:374)alit(cid:455) of a fi(cid:374)ite set. B= {1, 2, 3, 4, 5, 6} so b= |6| Definition: the set of all (different) subsets of s is the power set of s, which we denote as p(s). If s is a finite set, we can prove that. : the empty set has 0 elements, and 1 subset.

Related Questions

Can someone please help me with this? I don't even think the ones I answered are correct.

I need help with these as soon as possible Please. Thank You!!

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e^-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
a. approximately the year 2093
b. approximately the year 2041
c. approximately the year 2088
d. approximately the year 2016

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
a. f ^-1(x) = (x - 20)/2
b. f ^-1(x) = x - 20
c. f ^-1(x) = (x/2) - 20
d. f ^-1(x) = (x/2) + 20

Q19. If f(x) = 4^x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
a. (log ₄ 12, 12)
b. (log ₄ 12, 4)
c. (log ₄ 12, 0)
d. (12, 12)

Q20. Find functions f and g so that f â g = H(x) = (5 - 2x³)².
a. f(x) = 5 - 2x³ ; g(x) = x²
b. f(x) = (5 - 2x)³ ; g(x) = x²
c. f(x) = x² ; g(x) = 5 - 2x³
d. f(x) = x³ ; g(x) = (5 - 2x)²

Q29. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = 9, y = 2, z = 5; (9, 2, 5)
b. x = 8, y = 4, z = 5; (8, 4, 5)
c. x = 4, y = 5, z = 4; (4, 5, 4)
d. x = 8, y = -4, z = -5; (8, -4, -5)

Q30. Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

a. x = 2, y = 3, z = -7; (2, 3, -7)
b. x = 1, y = 3, z = -4; (1, 3, -4)
c. x = 5, y = 13/2, z = -3; (5, 13/2, -3)
d. x = 1, y = -3, z = -16; (1, -3, -16)

Q33. Write the partial fraction decomposition of the rational expression (4x³ + 4x²)/(x² + 5)².
a. (4x - 4)/(x² + 5) + (-20x + 20)/(x² + 5)²
b. (4x + 4)/(x² + 5) + (-20x - 20)/(x² + 5)²
c. (4x + 4)/(x² + 5) + (20x - 20)/(x² + 5)²
d. (4x + 4)/(x² + 5) + (20x + 20)/(x² + 5)²

Q34. Solve the linear programming problem. Minimize z = 11x + 6y + 7 subject to: x = 0, y = 0, x + y = 1.
a. minimum: 7
b. minimum: 18
c. minimum: 24
d. minimum: 13

Q35. Solve the system of equations by elimination.

a. x = 10, y = 0; (10, 0)
b. x = 10, y = 10; (10, 10)
c. x = 0, y = 10; (0, 10)
d. x = 0, y = 0; (0, 0)

Q36. Perform the row operations on the given augmented matrix.

a.
b.
c.
d.

Q37. Solve the system of equations using Cramer's Rule if it is applicable.

a. x = -4, y = 3; (-4, 3)
b. x = -3, y = -4; (-3, -4)
c. x = 4, y = 3; (4, 3)
d. x = 3, y = 4; (3, 4)

Q38. Write the partial fraction decomposition of the rational expression x/(x² - 9x + 20).
a. -4/(x - 4) + 5/(x - 5)
b. -5/(x - 4) + 4/(x - 5)
c. 4/(x - 4) + -5/(x - 5)
d. -4/(x - 4) + -5/(x - 5)

Q39. Solve the system of equations.

a. x = -4, y = 4, z = -3; (-4, 4, -3)
b. x = -3, y = 4, z = -4; (-3, 4, -4)
c. x = -4, y = -3, z = 4; (-4, -3, 4)
d. inconsistent

Q40. Find the value of the determinant.

a. 224
b. 24
c. -72
d. 72