IfA={a,b,c,d} , the number of anti-symmetric relations 2n×3m, then m+n=

A={a,b,c,d}⇒n(A)=4Number of anti-symmetric relations =2n⋅3n(n−1)2=24×34×32=24×36Comparing 2m×3n⇒m=4; n=6⇒m+n=10

IfA={a,b,c,d} , the number of anti-symmetric relations 2n×3m, then m+n=

A={a,b,c,d}⇒n(A)=4Number of anti-symmetric relations =2n⋅3n(n−1)2=24×34×32=24×36Comparing 2m×3n⇒m=4; n=6⇒m+n=10

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If $A = {a, b, c, d}$ , the number of anti-symmetric relations $2^{n} \times 3^{m}$ , then $m + n =$

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$A = {a, b, c, d} \Rightarrow n (A) = 4$

Number of anti-symmetric relations $= 2^{n} \cdot 3^{\frac{n (n - 1)}{2}}$

$= 2^{4} \times 3^{\frac{4 \times 3}{2}} = 2^{4} \times 3^{6}$

Comparing $2^{m} \times 3^{n} \Rightarrow m = 4; n = 6 \Rightarrow m + n = 10$

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If $A = {a, b, c, d}$ , the number of anti-symmetric relations $2^{n} \times 3^{m}$ , then $m + n =$