Question

If A ={1,2,3,4,}; B= { 3,4,5,6} THEN FIND n(A∆B)​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

$\rm :\longmapsto\:A = \{1,2,3,4 \} \\ \\ \rm :\longmapsto\:B= \{3,4,5,6\}$

Now, Consider

$\red{\rm :\longmapsto\:A - B}$

$\red{\rm \: = \:\{1,2,3,4,\} \: - \: \{ 3,4,5,6\}}$

$\red{\rm \: = \:\{1,2\}}$

Now, Consider

$\green{\rm :\longmapsto\:B - A}$

$\green{\rm \: = \: \{3,4,5,6\} - \{1,2,3,4\}}$

$\green{\rm \: = \: \{5,6\}}$

Now, Consider

$\purple{\rm :\longmapsto\:A \: \triangle \: B}$

$\purple{\rm \: = \: (A - B)\cup (B - A) \: }$

$\purple{\rm \: = \: \{1,2,5,6\}}$

Thus,

$\purple{\rm \implies\:\boxed{ \tt{ \: A \: \triangle \: B \: = \:\{1,2,5,6 \: \}}} }$

$\purple{\rm \implies\:\boxed{ \tt{ \:n( A \: \triangle \: B) \: = \:4 \: }} }$

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Additional Information :-

1. Commutative Law

$\red{\rm :\longmapsto\:A\cup B = B\cup A}$

$\red{\rm :\longmapsto\:A\cap B = B\cap A}$

2. Distributive Law

$\red{\rm :\longmapsto\:A\cup (B\cap C) = (A\cup B)\cap (A\cup C) \: }$

$\red{\rm :\longmapsto\:A\cap (B\cup C) = (A\cap B)\cup (A\cap C) \: }$

3. Associative Law

$\red{\rm :\longmapsto\:A\cup (B\cup C) \: = \: (A\cup B)\cup C \: }$

$\red{\rm :\longmapsto\:A\cap (B\cap C) \: = \: (A\cap B)\cap C \: }$

4. De Morgans Law

$\red{\rm :\longmapsto\:(A\cup B)' = A'\cap B' \: }$

$\red{\rm :\longmapsto\:(A\cap B)' = A'\cup B' \: }$