Set Theory Quiz for Algebra Class 10

False (B)

False (B)

<p>True (A)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>{2, 4, 6, 8, 10}</p> Signup and view all the answers

<p>A'</p> Signup and view all the answers

<p>Complement of a set A with respect to U = The set of all elements in U that are not in A Disjoint sets = Sets with no common elements Universal set = The set containing all elements under consideration</p> Signup and view all the answers

<p>intersection</p> Signup and view all the answers

<p>A ∩ B = The set containing elements found in both A and B. A ∪ B = The set containing all elements from A and B. A - B = The set containing elements found in A but not in B.</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Inverse law (B)</p> Signup and view all the answers

<p>{ 1, 2 }</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>and</p> Signup and view all the answers

<p>A shaded region within A, but not touching B. (B)</p> Signup and view all the answers

<p>-5 (B), 5 (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>T</p> Signup and view all the answers

<p>including</p> Signup and view all the answers

<p>{x : –3 &lt; x &lt; 5} (D)</p> Signup and view all the answers

<p>(–∞, 0) = {x : x &lt; 0} [0, ∞) = {x : x ≥ 0} (a, b) = {x : a &lt; x &lt; b} [a, b] = {x : a ≤ x ≤ b}</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>The set of real numbers</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Gottlob Frege (B)</p> Signup and view all the answers

<p>Russell's Paradox</p> Signup and view all the answers

<p>Ernst Zermelo</p> Signup and view all the answers

<p>Georg Cantor = Originated modern set theory Richard Dedekind = Supported Cantor's work Gottlob Frege = Presented set theory as logical principles Bertrand Russell = Discovered Russell's Paradox Ernst Zermelo = Published the first axiomatization of set theory</p> Signup and view all the answers

<p>(A ∪ B)′ = A′ ∪ B′ (B), (A ∩ B)′ = A′ ∩ B′ (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>Set theoretic language</p> Signup and view all the answers

<p>{2, 4} (C), {2, 4, 6} (D)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>{1, 2, 3, 4, 5}</p> Signup and view all the answers

<p>difference</p> Signup and view all the answers

<p>Distributive property of union over intersection: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (C)</p> Signup and view all the answers

<p>Union = A ∪ B Intersection = A ∩ B Difference = A - B Complement = A'</p> Signup and view all the answers

<p>The union of two sets is the set of elements that are in either set or both. (D)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>{3, 4}</p> Signup and view all the answers

<p>union</p> Signup and view all the answers

<p>A ∪ B = B ∪ A = Commutative law (A ∪ B) ∪ C = A ∪ (B ∪ C) = Associative law A ∪ φ = A = Law of identity element A ∪ A = A = Idempotent law U ∪ A = U = Law of U</p> Signup and view all the answers

<p>{Geeta} (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}</p> Signup and view all the answers

The union of two sets A and B includes all elements in A or B or both.

If B is a subset of A, the union of A and B equals A.

A ∪ B = { x : x ∈ A or x ∈ B } shows union definition using set notation.

A ∪ B = B ∪ A illustrates the order of union does not matter.

(A ∪ B) ∪ C = A ∪ (B ∪ C) shows grouping does not impact union.

A ∪ φ = A indicates A remains unchanged when unioned with the empty set.

The intersection of sets A and B consists of elements common to both A and B.

A ∩ B = { x : x ∈ A and x ∈ B } describes intersection using set notation.

Two sets A and B are disjoint if A ∩ B = φ, meaning they have no elements in common.

A ∩ B = B ∩ A; the order of intersection does not matter.

(A ∩ B) ∩ C = A ∩ (B ∩ C); how sets are grouped does not affect intersection.

The difference A - B is the set of elements in A but not in B.

A visual tool to show relationships between sets, including intersections and differences.

A ∩ A = A; the intersection of a set with itself is the set.

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C); intersection distributes over union.

Rational numbers can be expressed as fractions a/b, where a and b are integers and b ≠ 0.

Irrational numbers cannot be expressed as fractions and include numbers like π and √2.

An open interval (a, b) includes all numbers y such that a < y < b, excluding a and b.

A closed interval [a, b] includes all numbers x such that a ≤ x ≤ b, including a and b.

Intervals can be mixed, e.g., [a, b) includes a but not b; (a, b] includes b but not a.

The length of an interval (a, b) is calculated as (b - a).

The universal set contains all possible elements relevant to a particular context.

Set-builder notation describes a set by a property that its members must satisfy, like {x : –5 < x ≤ 7}.

The set of real numbers that are not rational numbers (irrational numbers).

The set of all elements in the universal set U that are not in set A, denoted as A′.

A set that contains all possible elements relevant to a particular discussion or problem.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {1, 3, 5, 7, 9}, then A′ = {2, 4, 6, 8, 10}.

To determine if two sets are disjoint, check if they share any elements.

A set A is a subset of set U if all elements of A are also in U.

Numbers that can divide 42 without leaving a remainder (1, 2, 3, 6, 7, 14, 21, 42).

For sets A and B, (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.

German mathematician credited with developing set theory.

Cantor showed the set of real numbers is larger than the integers.

The contradiction arising from assuming a set of all sets exists.

Formal principles established to avoid paradoxes in set theory.

Mathematician who published the first axiomatisation of set theory in 1908.

A modified axiomatisation of set theory that addressed earlier paradoxes.

Modern mathematics often uses set theory for expressing concepts.

A set that does not contain any elements, denoted as φ.

A set with a definite number of elements.

A set that has no end and cannot be counted completely.

A set A is a subset of set B if every element of A is also in B.

Two sets A and B are equal if they contain the exact same elements.

The union of sets A and B includes all elements that are in A, B, or both.

The intersection of sets A and B includes only the elements common to both sets.

The difference of sets A and B (A - B) includes elements in A but not in B.