Math, asked by ISHAFIROZKHAN, 8 months ago

4. Consider the set A = {-1, 1}.
a) Write all elements in A x A. ……1
b) How many relations are there from A to A? ……….1
c) Write all functions from A to A

Answers

Answered by Mathematically
14

Step-by-step explanation:

Set A = {-1,1}

a) (A×A) = {(-1,-1), (-1,1), (1,-1), (1,1)}

b) Number of relations from A to A = 2^cardinality

= 2^4

= 16

c) f(A to A) = {(-1,-1),(1,1)}

= {(-1,1),(1,1)}

= {(-1,-1),(1,-1)}

= {(-1,1),(1,-1)}

Answered by isha00333
4

Given: Set \[A = \left\{ { - 1,1} \right\}\].

Solution:

Part a:

Find all elements of \[A \times A\].

\[\left\{ {A \times A} \right\} = \left\{ {\left( { - 1, - 1} \right),\left( { - 1,1} \right),\left( {1, - 1} \right),\left( {1,1} \right)} \right\}\]

Part b:

Find the number of relation from A to A.

Number of relations from A to A \[ = {2^{no, of possible relations}}\]

                                                     \[\begin{array}{l} = {2^4}\\ = 16\end{array}\]

Part c:

Write all the functions from \[f\left( {A\,\,to\,\,A} \right).

\[\begin{array}{l}\left\{ {\left( { - 1, - 1} \right),\left( {1,1} \right)} \right\}\\\left\{ {\left( { - 1,1} \right),\left( {1,1} \right)} \right\}\\\left\{ {\left( { - 1, - 1} \right),\left( {1, - 1} \right)} \right\}\\\left\{ {\left( { - 1,1} \right),\left( {1, - 1} \right)} \right\}\end{array}\]

Similar questions