Discrete mathematical relation operation

设 A = { a , b , c } , B = { b , c , d } , C = { d , e , f } , R 1 = { < 1 , 2 > , < 2 , 2 > , < 2 , 3 > , < 3 , 3 > } , R 2 = { < 2 , 2 > , < 2 , 3 > , < 3 , 4 > } 求 设A=\{a,b,c\},B=\{b,c,d\},C=\{d,e,f\},R_1=\{<1,2>,<2,2>,<2,3>,<3,3>\},R_2=\{<2,2>,<2,3>,<3,4>\}求 Let A={ a,b,c},B={ b,c,d},C={ d,e,f},R1​={ <1,2>,<2,2>,<2,3>,<3,3>},R2​={ <2,2>,<2,3>,<3,4>} Seeking

$1.A\cup B$

Find the union of two sets

A ∪ B = { a , b , c , d } A\cup B=\{a,b,c,d\} A∪B={ a,b,c,d}

$2.A⨁B$

Find the symmetric difference, that is, find the unique elements of the two sets, that is, the union of the two sets minus the intersection of the two sets

$A⨁B=\{a,d\}$

$3.R_1^{-1}$

Find the relationship $R_1$The inverse relationship of $R_1$All the elements in can be reversed

R 1 − 1 = { < 2 , 1 > , < 2 , 2 > , < 3 , 2 > , < 3 , 3 > } R_1^{-1}=\{<2,1>,<2,2>,<3,2>,<3,3>\} R1−1​={ <2,1>,<2,2>,<3,2>,<3,3>}

$4.R_1\cdot R_2$

Find the intersection of two relations, that is, the common elements in the two relation sets

$R_1\cdot R_2=<2,2>,<2,3>$

$R_{1}InAonthelimitsystem$

$R_1$In $A$ limitation is the empty set on