IAT (IISER) Maths Marathon Complete Revision - CUET Maths

Mathematics Concepts and Problem-Solving for Aptitude Tests

Relations and Functions Relations and functions are foundational concepts in mathematics, especially in set theory and algebra. The transcript discusses how to determine whether a given relation is a function, reflexive, symmetric, or transitive, and how to check for equivalence relations....

The area of the region enclosed between the curves $4x^2=y$ and $y=4$ is:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>16</mn><mn>3</mn></mfrac></math> sq. units

Given the relation on set A = {1, 2, 3, 4} defined by the pairs (1,3), (4,2), (2,4), (2,3), (3,1), which property does this relation satisfy?

It is not symmetric

The area of the region enclosed between the curves $4x^2=y$ and $y=4$ is:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>16</mn><mn>3</mn></mfrac></math> sq. units

Given the relation on set A = {1, 2, 3, 4} defined by the pairs (1,3), (4,2), (2,4), (2,3), (3,1), which property does this relation satisfy?

It is not symmetric

What defines a Reflexive Relation on a set $A$?

A relation $R$ on a set $A$ is reflexive if for every element $a \in A$, the ordered pair $(a,a)$ is an element of $R$. This means every element is related to itself.

What three properties must a relation satisfy to be classified as an Equivalence Relation?

An equivalence relation must be reflexive, symmetric, and transitive. This means it must satisfy $(a,a) \in R$, if $(a,b) \in R$ then $(b,a) \in R$, and if $(a,b) \in R$ and $(b,c) \in R$ then $(a,c) \in R$.