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 âˆˆ Z

This shows that 5 is an element (âˆˆ) of the set of integers (Z)

Y is a multiple of 10

Y = 10k, k âˆˆ 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 âˆˆ (x âˆ© y). [A is in the intersection of x and y, which means it belongs to both of them]

We can also use (A âˆˆ x) âˆ§ (A âˆˆ y). The âˆ§ 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 â‰¤ y â‰¤ 5

The square of the difference of x and y is not more than 10

(x-y)Â² â‰¤ 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

xÂ² > 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 âˆˆ Z

7 is an odd number

Odd numbers are just even numbers + / - 1, so we use:

7 = 2k + 1, k âˆˆ Z

1/4 is a rational number

The set of rational numbers is Q, so

1/4 âˆˆ Q

Hope this helps!