(1 point) consider the universal set u={1,2,3,4,5,6,7,8,9,10}, define the set a be the even numbers, the set b be the odd numbers, and the set c={4,5,6}. complete the following exercises in set notation.
(a) a u c
(b) b n c
(c) a n b
(d) b - c

a) AUC = {2,4,6,8,10}

b) BnC = {}

c) AnB = {}

d) B-C = B = {1,3,5,7,9}

Step-by-step explanation:

The set A is the even numbers, those that are divisible by two.

So A = {2,4,6,8,10}

B is the odd numbe.rs. An odd number is a number that is not divisible by two.

So B = {1,3,5,7,9}.

C = {4,5,6}, as the problem states

a) The union of sets is a set containing all elements that are in at least one of the sets. So the union of A and C is a set that contains all elements that are in at least one of A or C.

So AUC = {2,4,6,8,10}.

b) The intersection of two sets consists of all elements that in both sets. So, the intersection of B and C is the set that contains all elements that are in both B and C.

There are no elements that are in both B and C, so the intersection is an empty set

BnC = {}

c) Same explanation as b), there are no elements that are in both A and B, so another empty set.

AnB = {}

d) The difference of sets B and C consists of all elements that are in B and not in C. We already have in b) that BnC = {}, so:

B-C = B = {1,3,5,7,9}

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step-by-step explanation:

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9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841