E only = 15 - 6 = 9
F only = 20 - 6 = 14

n(E∪F) is the addition of all the numbers in the rectangle.

n(E∪F) = 9 + 6 + 14 = 29

Whole numbers

Whole numbers is a collection of all the basic counting numbers and 0. In mathematics, counting numbers are called natural numbers. So, we can define the whole number as a collection of all natural numbers and 0. Whole numbers also include all positive integers along with zero.

Composite numbers

In math, composite numbers can be defined as numbers that have more than two factors. Numbers that are not prime are composite numbers because they are divisible by more than two numbers.

Natural numbers

Natural numbers are all positive integers from 1 to infinity. They are also called counting numbers as they are used to count objects. Natural numbers do not include 0 or negative numbers. We need numbers in our everyday life, be it for counting objects, telling time, or numbering houses.

Integers

Is a whole number (not a fractional number) that can be positive, negative, or zero.

As you can see from the definitions, an integer could be a whole number, could be a composite number or natural number. Whole numbers, composite numbers and natural numbers are all subset of integers

Intersection (∩) are elements you can find in both sets.

n in n(A∩B) means the number of elements. So you count how many elements are in A∩B once you are done finding the elements.

A = {1, 3, 5, 7, 9, 11, 13, 15}
B = {3, 6, 9, 12, 15}

As you can see 3, 9 and 15 are the only elements that can be seen in both the sets A and B

Hence A∩B = {3,9,15}

Since you are asked how many elements (n), you count how many elements are in {3,9,15} and I believe you've counted three

Hence n(A∩B) = 3

Since the set P is equal to the set Q, thus P = Q, it means all the elements in P is in Q and all the elements in Q is also in P. So you simply have to find which element is in P but not in Q.

P = {4, 8, 12, 16, 20}

Q = {16, 4, 12, k, 20}

Since the elements of P are arranged from the smallest to the largest, let's arrange Q too as well

⇒ Q = {4, k, 12, 16, 20}

P = {4, 8, 12, 16, 20}

As you can see the missing element (k) in Q is 8

x:x is read as x is such that x is ...

N contains the list of factors of 18. A factor is a number or algebraic expression that divides another number or expression evenly, thus no remainder.

Factors of 18 are 1,2,3,6,9 and 18 itself

Thus

1x18 = 18

2x9 = 18

3x6 = 18

Hence 1,2,3,6,9 and 18 are factors of 18

⇒ N = {1,2,3,6,9,18}

Multiples of 12 are numbers 12 can divide without a remainder (Simply the multiplication of 12). If you don't know the recitation of the multiples, simply add 12 to the preceding numbers to get the subsequent numbers starting from 12.

Multiples of 12

12,12+12=24,24+12 = 36,36+12 = 48,48+12 = 60,60+12 = 72,72+12 = 84,84+12 = 96,96+12 = 108,108+12 = 120,120+12 = 132,132+12 = 144,...

⇒ multiples of 12 are 12,24,36,48,60,72,84,96,108,120,132,144,...

⇒ M = {12,24,36,48,60,72,84,96,108,120,132,144,...}

∩ means intersection. The element(s) which you can find in both sets.

Hence N ∩ M should contain element(s) which can be found in both set N and M.

From the above, you can see that there is no element that can be found in N,{1,2,3,6,9,18} and at the same time be found in M,{12,24,36,48,60,72,84,96,108,120,132,144,...}. Hence the intersection of N and M is an empty set {}

Union (∪) is the arrangement from the lowest to the highest of the elements in both sets. If an element occurs in both sets, its written only once

P = {7,11,13} and Q = {9,11,13}

⇒ P ∪ Q = {7,9,11,13}

Intersection (∩) are elements you can find in both sets.

n in n(A∩B) means the number of elements. So you count how many elements are in A∩B once you are done finding the elements.

A = {1, 3, 5, 7, 9, 11, 13, 15}
B = {3, 6, 9, 12, 15}

As you can see 3, 9 and 15 are the only elements that can be seen in both the sets A and B

Hence A∩B = {3,9,15}

Since you are asked how many elements (n), you count how many elements are in {3,9,15} and I believe you've counted three

Hence n(A∩B) = 3

Since the set P is equal to the set Q, thus P = Q, it means all the elements in P is in Q and all the elements in Q is also in P. So you simply have to find which element is in P but not in Q.

P = {4, 8, 12, 16, 20}

Q = {16, 4, 12, k, 20}

Since the elements of P are arranged from the smallest to the largest, let's arrange Q too as well

⇒ Q = {4, k, 12, 16, 20}

P = {4, 8, 12, 16, 20}

As you can see the missing element (k) in Q is 8