If A B = a, b, B A = c, d and A B = e, f, then the set B is equal to

Question

If A B = a, b, B A = c, d and A B = e, f, then the set B is equal to (A) a, b, c, d (B) e, f, c, d (C) a, b, e, f (D) c, d, a, e

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Given, A / B = a, b B / A= C, d and A ∩ B= e, f ∴ A-B= a, b ....(i) B-A= c, d ....(ii) and A ∩ B= e, f ...(iii) ∴ From Eqs. (i), (ii) and (iii), we get B= c, d, e, f <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d27652639afd0da5da6e83e97bb98681-.png" />

Q. If A\B = {a, b}, B\A = {c, d} and A\B = {e, f}, then the set B is equal to

{a, b, c, d}

{e, f, c, d}

{a, b, e, f}

{c, d, a, e}

{d, e, a, b}

Given, $A / B = {a, b}$
$B / A = {C, d}$
and $A \cap B = {e, f}$
$∴ A - B = {a, b} .... (i)$
$B - A = {c, d} .... (ii)$
and $A \cap B = {e, f} ... (iii)$
$∴$ From Eqs. (i), (ii) and (iii), we get
$B = {c, d, e, f}$