Question

If R is a relation 'is greater than' A from A={4, 5, 6, 7} to B = {1,3,5,7}, write R as set of ordered pairs, also find inverse relation to R.​

Answer 1

Answer :

R is a relation where

Elements of A > Elements of B

A = {4,5,6,7} & B = {1,3,5,7}

Where A is a domain

& B is a range

So we are making sets of element greater

{4 > 1, 4 > 3, 5 > 1, 5 > 3, 6 > 1, 6 > 3, 6 > 5, 7 > 1, 7 > 3, 7 > 5}

R = {(4, 1) , (4, 3) , (5, 1) , (5, 3) , (6, 1) , (6, 3) , (6, 5) , (7, 1) , (7, 3) , (7, 5) }

R inverse

$R^{-1}$ = {(1, 4) , (3, 4) , (1, 5) , (3, 5) , (1, 6) , (3, 6) , (5, 6) , (1, 7) , (3, 7) , (5, 7)}

Answer 2

Answer :

R is a relation where

Elements of A > Elements of B

A = {4,5,6,7} & B = {1,3,5,7}

Where A is a domain

& B is a range

So we are making sets of element greater

{4 > 1, 4 > 3, 5 > 1, 5 > 3, 6 > 1, 6 > 3, 6 > 5, 7 > 1, 7 > 3, 7 > 5}

R = {(4, 1) , (4, 3) , (5, 1) , (5, 3) , (6, 1) , (6, 3) , (6, 5) , (7, 1) , (7, 3) , (7, 5) }

R inverse

R^{-1}R

−1

= {(1, 4) , (3, 4) , (1, 5) , (3, 5) , (1, 6) , (3, 6) , (5, 6) , (1, 7) , (3, 7) , (5, 7)}