Set A = {1, 2, 3, 4, 5, 6, 7}

If number of functions from set A to power set of A can be expressed as mⁿ (m is least integer). Find m + n.

n P (A) = 2⁷ = 128

f : A → B

Number of function = 128 × 128….128 = 128⁷

$={\left(2^7\right)}^7=2^{49}$

->mⁿ = 2⁴⁹

m + n = 49 + 2 = 51

<p><span lang="EN-IN">n P (A) = 2⁷ = 128</span></p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1759128393phpRNCMJq.jpeg" alt="" width="223" height="193" loading="lazy"></picture></div></div><p><span lang="EN-IN">f : A → B</span></p><p><span lang="EN-IN">Number of function = 128 × 128….128 = 128⁷</span></p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <msup> <mrow> <mn>2</mn> </mrow> <mrow> <mn>7</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>7</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mn>2</mn> </mrow> <mrow> <mn>4</mn> <mn>9</mn> </mrow> </msup> </mrow> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820653760"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</span></p><p><span lang="EN-IN">-&gt;mⁿ = 2⁴⁹</span></p><p><span lang="EN-IN">m + n = 49 + 2 = 51</span></p>

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