## Sunday, 4 August 2013

3y^2-14y+8

3y^2-14y+8
Solution
=3y^2-14y+8
=3y^2-12y-2y+8
= 3y(y-4)-2(y-4)
=(y-4)(3y-2)

### Given A = {1,2,3}, B = {1,2,3,4,5}, and C = { 4, 5, 6, 7}. Evaluate each set a) A ∩ B b) A U C c) B U C d) (A U B) ∩ C e) A U (B U C) f) (A ∩ B) ∩ C g) (A ∩ B) U C

Given A = {1,2,3}, B = {1,2,3,4,5}, and C = { 4, 5, 6, 7}. Evaluate each set
a) A ∩ B
b) A U C
c) B U C
d) (A U B) ∩ C
e) A U (B U C)
f) (A ∩ B) ∩ C
g) (A ∩ B) U C

a) A ∩ B
Solution
A ∩ B = {1,2,3} ∩ {1,2,3,4,5}
A ∩ B = {1,2,3}
b) A U C
solution
A U C = {1,2,3} U { 4, 5, 6, 7}
A U C = {1,2,3,4,5,6,7}
c) B U C
Solution
B U C = {1,2,3,4,5} U { 4, 5, 6, 7}
B U C ={1,2,3,4,5,6,7}
d) (A U B) ∩ C
(A U B) ∩ C = [{1,2,3} U {1,2,3,4,5}] ∩ { 4, 5, 6, 7}
(A U B) ∩ C = {1,2,3,4,5} ∩ { 4, 5, 6, 7}
(A U B) ∩ C ={4,5}
e) A U (B U C)
Solution
A U (B U C) ={1,2,3} U [{1,2,3,4,5} U { 4, 5, 6, 7}]
A U (B U C) = {1,2,3} U {1,2,3,4,5,6,7}
A U (B U C) = {1,2,3,4,5,6,7}
f) (A ∩ B) ∩ C
Solution
(A ∩ B) ∩ C = [{1,2,3} ∩{1,2,3,4,5}] ∩ { 4, 5, 6, 7}
(A ∩ B) ∩ C = {1,2,3} ∩ { 4, 5, 6, 7}
(A ∩ B) ∩ C = { }
g) (A ∩ B) U C
Solution
(A ∩ B) U C = [{1,2,3} ∩{1,2,3,4,5}] U { 4, 5, 6, 7}
(A ∩ B) U C = {1,2,3} U { 4, 5, 6, 7}
(A ∩ B) U C = {1,2,3,4,5,6,7}