Let A={2,3,4} B={2,5,6} C={5,6,2} and D={6}. Determine if the following statements are true: i). 4€C
ii). 5€C
iii). A=B
iv). B=C

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True

Step-by-step explanation:

Given sets are:

Lets look at the statements one by one.

i. 4∈C

This statement means that 4 is a member of set C. Looking at the members of set C, it can be concluded that the statement is wrong as C doesn't contain 4.

ii. 5∈C

This statement is true as 5 is a member of C.

iii. A=B

This statement states that set A is equal to set B. Two sets are said to be equal if there number of elements and members are same. Set A and Set B have different members so this statement is false.

iv. B=C

Set B and Set C have equal number of members and the members (5,6,2) are also same so the statement is true.

Hence,

i. 4∈C => False

ii. 5∈C => True

iii. A = B => False

iv. B=C => True

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.