List the elements of the following sets

where P = {1,2,3...}

A={x:x € P, 3 < x < 12}
B={x:x € P, x is even, x < 15}
C={x:x € P, 4 + x € 3}
D={x:x € P, x is multiple of 5}

x∈P means x stands for a positive integer.

since x∈A means 3<x<12,
A={4,5,6,7,8,9,10,11}

You can do B,C, and D similarly.

True

can you give me the answer please

A = {4, 5, 6, 7, 8, 9, 10, 11}

B = {2, 4, 6, 8, 10, 12, 14}
C = {1} (since 4 + 1 = 5, which is not in P)
D = {5, 10, 15, 20, 25, 30...} (basically, all the numbers in P that are multiples of 5)

To find the elements of each set, we need to follow the given conditions for each set.

A = {x : x ∈ P, 3 < x < 12}
To find the elements of set A, we look for all the numbers that belong to the set P (positive integers) and satisfy the condition that 3 < x < 12.

The elements of set A are:
A = {4, 5, 6, 7, 8, 9, 10, 11}

B = {x : x ∈ P, x is even, x < 15}
For set B, we need to find all the even numbers less than 15 from set P.

The elements of set B are:
B = {2, 4, 6, 8, 10, 12, 14}

C = {x : x ∈ P, 4 + x ∈ 3}
To find the elements of set C, we look for numbers in set P for which the sum of 4 and the number is divisible by 3.

The elements of set C are:
C = {2, 5, 8, 11, 14, ...}

D = {x : x ∈ P, x is multiple of 5}
For set D, we need to find all the numbers from set P that are multiples of 5.

The elements of set D are:
D = {5, 10, 15, 20, 25, ...}

Please note that the set C will have infinite numbers since for any number 'x' that satisfies the condition, '4 + x' will always be divisible by 3. Therefore, the set C continues indefinitely.