Question

Consider the set {-3, 3}.

i) Write all elements in AXA

ii) How many relations are there from A to A ?

iii) Write all functions fron A to A which has range {-3, 3}, using arrow diagram.​

Answer 1

Answer:

(i) A×A = {(-3,-3),(-3,3),(3,-3),(3,3)}

(ii) Number of relations = 2⁴ = 16

(iii) A×A = {(-3,-3),(-3,3),(3,-3),(3,3)}

Step-by-step explanation:

(i) A×A = {(-3,-3),(-3,3),(3,-3),(3,3)}

A×A = {(x,y):x, y€A}

(ii) The total number of relations that can be

defined from a set A to a set A is the number of

possible subsets of A × A. Given, n(A ) = 2,

then (A × A) = 2² = 4 and the total number of

relations is 2⁴=16 .

(iii) According to the question,

A×A = {(x,y):x, y€A}

in roster form, A×A = {(-3,-3),(-3,3),(3,-3),(3,3)}

domain= elements of set A