Relations

Just basic stuff. Suitable for revision for JEE, IAT, NEST. Question mode: Flashcards only. Answer Mode: Answer with definition. Good luck!

What is the number of elements in the cartesian product of A and B if A has m elements and B has n elements?

n(A\times B)=m\times n=mn elements

What is the number of possible relations for A\times B if A has m elements and B has n elements?

2^{mn}

In A\times B, what is the domain?

A

In A\times B, what is the codomain?

B

What is a Reflexive Relation?

A relation R on set A is said to be reflexive if every element of A is related to itself.

Thus, (a,a) \in R

What is a Symmetric Relation?

A relation R on set A is said to be symmetric if

(a,b)\in R \implies (b,a)\in R

What is a Transitive Relation?

A relation R on set A is said to be transitive if

[(a,b)\in R and (b,c)\in R]\implies (a,c)\in R

What is an Equivalence Relation?

If a relation is reflexive, symmetric, and transitive then it is an equivalence relation

What is an Identity Relation?

A relation is an Identity Relation if

I_A=\{(a,a), a\in A\}