Sets | MCQs

Explanation

The empty set is a set with no elements.

It is denoted by { } or Ø.

Explanation

The expression {x|x ∈ A ∨ x ∈ B} represents the set of elements that are in A or in B or in both.

This is the definition of the union of two sets, denoted as A ∪ B.

Explanation

The intersection of two sets X and Y (X ∩ Y) is the set of elements that are common to both X and Y.

Given:

X = {2, 4, 6, 8}

Y = {1, 2, 3, 6}

The common elements are 2 and 6.

So, X ∩ Y = {2, 6}.

Explanation

Explanation

To find the intersection (C ∩ D) of sets C and D, we need to find the elements that are common to both sets.

C = {a, b, e, f}

D = {2, 4, 8, 10}

Since there are no common elements between C and D, the intersection is an empty set.

Explanation

The set $left{frac{p}{q} : p, q in mathbb{Z}, q neq 0right}$ represents the set of rational numbers.

Rational Numbers: A number is considered rational if expressed as the quotient $frac{p}{q}$, where $p$ and $q$ are integers and $q\mathrm{\ne }0$

This set includes numbers like $frac{1}{2}$, $-frac{3}{4}$, and $7$ (which can be written as $frac{7}{1}$).

Explanation

The set of positive integers is commonly referred to as the natural numbers or counting numbers

It is denoted by the symbol N or Z+.

This set includes all whole numbers greater than zero: 1, 2, 3, and so on. 

Explanation

The set of all natural numbers, together with zer,o is the set of whole numbers

Explanation

Natural numbers are also commonly called counting numbers.

They are the positive integers {1, 2, 3, ...}.

Sometimes, depending on the definition, they may also be referred to as positive integers or non-negative integers when including zero

Explanation

The power set of a nonempty set X is the set of all subsets of X, including X itself and the empty set. It forms a topology on X.