Question

6. Find the symmetric difference between the following set P={2,3,5,7,11} and Q={1,3,5,11}.​

Answer 1

Step-by-step explanation:

(i) P = {2, 3, 5, 7, 11} Q = {1, 3, 5, 11} P – Q = {2, 3, 5, 7, 11} – {1, 3, 5, 11} = {2, 7} Q – P = {1, 3, 5, 11} – {2, 3, 5, 7, 11} = {1} P Δ Q = (P – Q) ∪ (Q – P) = {2, 7} ∪ {1} = {1, 2, 7} (ii) R = {l, m, n, o, p} S = {j, l, n, q} R – S = {l, m, n, o, p} – {j, l, n, q} = {m, o, p} S – R = {j, l, n, q)} – {l, m, n, o, p}= {j, q} R Δ S = (R – S) ∪ (S – R) = {m, o, p} ∪ {j, q} = {j, m, o, p, q} (iii) X = {5, 6, 7} Y = {5, 7, 9, 10} X – Y = {5, 6, 7} – {5, 7, 9, 10} – {6} Y – X = {5, 6, 9, 10} – {5, 6, 7} = {9, 10} X Δ Y = (X – Y) ∪ (Y – X) = {6} ∪ {9, 10} = {6, 9, 10}.