Hi! I can't type the fancy forms of R, Q, Z, and other groups, but I hope you understand what I mean by them.
5 is an integer
5 ∈ Z
This shows that 5 is an element (∈) of the set of integers (Z)
Y is a multiple of 10
Y = 10k, k ∈ Z
This means that Y = 10 x k, where k is an integer, which is the definition of a multiple.
A belongs to both sets x and y
We can use A ∈ (x ∩ y). [A is in the intersection of x and y, which means it belongs to both of them]
We can also use (A ∈ x) ∧ (A ∈ y). The ∧ means "and", so this reads as "A is in x and A is in y".
The values of y range feom -4 to 5
-4 ≤ y ≤ 5
The square of the difference of x and y is not more than 10
(x-y)² ≤ 10
Notice that "not more" translates to "less than or equal to", and not just "less than", since the square of the difference could be equal to 10.
The square of a number is positive
x² > 0
Positive translates to "> 0". Interestingly enough, this statement is FALSE. Since x could be 0, x^2 could be 0, which is not positive.
8 is an even number
An even number means that it is a multiple of 2, so similar to earlier,
8 = 2k, k ∈ Z
7 is an odd number
Odd numbers are just even numbers + / - 1, so we use:
7 = 2k + 1, k ∈ Z
1/4 is a rational number
The set of rational numbers is Q, so
1/4 ∈ Q
Hope this helps!
