Question

Find the symmetric difference between the following sets.
(i) P = {2, 3, 5, 7, 11} and Q={1, 3, 5, 11}
(ii) R = {l, m, n, o, p} and S = {j, l, n, q}
(iii) X = {5, 6, 7} and Y={5, 7, 9, 10}

Answer 1

Solution:-

Symemetric diffrence:- Let A and B are two sets. The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B.

Thus, A △ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}

(i) P = {2, 3, 5, 7, 11} and Q={1, 3, 5, 11}

》Ans:- (P- Q )= {2,7} (Q-P) = { 1,}

》 ( P△Q )= {1,2,7} ans

(ii) ) R = {l, m, n, o, p} and S = {j, l, n, q}

》Ans:- (R-S ) = {m,o,p} (S-R) = { J,q}

》(R△S ) = {j,m,o,p,q} ans

(iii)X = {5, 6, 7} and Y={5, 7, 9, 10}

》Ans:- (X-Y) = {6} (Y-X) = { 9 , 10}

》(X△Y )= {6,7,10} ans


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