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)

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

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}

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}

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