Question

Given the following binary relations: The relation Rl on {w, 1, y, z), where R1 = {(w, w), (w, 1), (x, w), (x, 1 ), (x, z), (y, y), (z,y),(2, 2)). The relation R2 on (a, b, c), where R2 = {(a, a ), (b, b), (c, c), (a, b), (a, c), (c, b)}. The relation R3 on {x,y,z}, where R3 = {(1, 2), (9,2), (2, y)}. Determine whether these relations are: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive?

Answer 1

solution:- Given that Reflective: for every element x present in set we should have a pair like love then that is reflexive symetrix: If CX, Y) poresent in R then we should have cY,x)in R anti- symmetonix: if (x,y) present in R then we should not have (y,x) in Rexcept x=y toransitive: if cX, YICY,Z) present in a the we should have ex, z) in a Rii foor every element x in set we have a paios like cx,x on RI So Riis reflexive cx, 27 is present in R, but czxo is not on so it is not symmetric poneront

(W x ) and cx, w) are present in r, so it is not anti symmetric cw, x 2(x, z 2 porcsont in Ribut cw, z ) IS NOT prosent so it is not toransitive di Re: for every eleminent xin set we have a paion like cx,x on RI SO R2 is reflexive (a, b),(a,c7cc blare present in R2 but (ba present so it is not cc,ar, Cb, c) are not symmetric iz is anti symmetric it is transitive R3: don't have a tot for every element x im set we a paior like cx,x 2 în R3 h at so R3 is not reflexive

(Y,Z) is peresent in R3 (2,7 318 also ponesent so it is symmetric IN and (z,y are present in R3 so it is not conti symmetoric (Y,Z) CZ,Y I poresent in R3 but CZ, Z) IS NOT poresont so it is not transitive - Thank you