Question

D and E are sets of real numbers defined as follows.D= x<2E = x Write D n E and DU E using interval notation.If the set is empty, write Ø.

Answer 1

A real number is a value of a continuous quantity that can represent a distance along a line. It includes all numbers, except complex numbers.

The set D is defined as all numbers less than 2, while the set E represents all the numbers greater than 5.

D ∩ E: This means the intersection of sets D and E. The intersection of two sets is the set of the elements that are in both sets.

Since D contains all numbers less than 2 and E contains all the numbers greater than 5, the intersection contains no elements, since no elements from D exist in E.

Hence,

`D\cap E=\varnothing`

D ∪ E: This means the union of sets D and E. The union of two sets contains all the elements contained in either set (or both sets).

The union of D and E includes all real numbers less than 2 (from set D) and all numbers greater than 5 (from set E).

In interval notation, it is given as:

`D\cup E=(-\infty,2)\cup(5,\infty)`