Let A = {1, {1}, 3, 4, {5, 6}} be a set, and let B and C be the following relations on A:            B = {(1, 3), (4, 1), (3, {5, 6}), ({1}, 4), ({5, 6}, {1})}            C = {(1, 1), (3, 4), (4, 3), ({5, 6}, {1})The relation C is irreflexive.a.Trueb.False

Let A = {1, {1}, 3, 4, {5, 6}} be a set, and let B and C be the following relations on A:            B = {(1, 3), (4, 1), (3, {5, 6}), ({1}, 4), ({5, 6}, {1})}            C = {(1, 1), (3, 4), (4, 3), ({5, 6}, {1})The relation B is antisymmetric.a.Trueb.False

Let A = {1, {1}, 3, 4, {5, 6}} be a set, and let B and C be the following relations on A:            B = {(1, 3), (4, 1), (3, {5, 6}), ({1}, 4), ({5, 6}, {1})}            C = {(1, 1), (3, 4), (4, 3), ({5, 6}, {1})The composition relation C;B is {(1, 3), (3, 1), (3, {5, 6}), ({5, 6}, 4)}.a.Trueb.False

Let A = {4,5,6} , B = {a,y,c,w}and R = {(4,c), (4,y), (5,a),(5,c), (5,w)} is a relation from A to B.Then we can write :

The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is __________Question 1Answerreflexive, symmetric and transitiveneither reflexive, nor irreflexive but transitiveirreflexive and antisymmetricirreflexive, symmetric and transitive

Let R1 be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:An element a in A is related to an element b in B (under R1) if a××b is divisible by 3.An element a in B is related to an element b in C (under R2) if a××b is even but not divisible by 3.Which is the composite relation R1R2 from A to C?Question 2AnswerR1R2 = {(2,2), (3, 2), (3, 4), (5, 1), (5, 3), (7, 1)}R1R2 = {(1, 2), (1, 4), (3, 3), (5, 4), (5,6), (7, 3)}ΦR1R2 = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)}