If A and B be two sets such that n(A) = 15, n(B) = 25, then number of possible values of (symmetric difference of A and B) is

JEE MainMathematicsToughSets

If A and B be two sets such that n(A) = 15, n(B) = 25, then
number of possible values of $n(A\Delta B)$ (symmetric difference of A
and B) is

Show answer and solution

n(A\Delta B) = n(A \cup B) - n(A \cap B)

for maximum

n(A\Delta B),n(A \cup B)

should be maximum and

n(A \cap B)

is minimum
For

n(A \cap B)

to be minimum,

A \cap B = \phi

\Rightarrow n(A \cup B) = 25 + 15 = 40

n(A\Delta B) = 40

For

n(A \cap B)

to be maximum,

A \subset B

n(A \cap B) = 15

\Rightarrow n(A \cup B) = 25

\Rightarrow n(A\Delta B) = 25 - 15 = 10

\Rightarrow \ Range\ of\ (A\Delta B) = \{ 10,\ 12,\ 14,\ 16,\ldots..,\ 40\}

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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