Number of correct statements among the following is . Then is ________ Statement I: For two given events A and B, is not less than . Statement II: The number of symmetric relations defined on the set {1,2,3,4} which are not reflexive is 20.

Question

Number of correct statements among the following is $k$ . Then $3 k$ is ________

Statement I: For two given events A and B, $P (A \cap B)$ is not less than $P (A) + P (B) - 1$ .

Statement II: The number of symmetric relations defined on the set {1,2,3,4} which are not reflexive is 20.

Statement III: $\lim_{n \to \infty} {(a^{\frac{1}{^{2}}} - a^{\frac{1}{^{3}}}) (a^{\frac{1}{^{2}}} - a^{\frac{1}{^{5}}}) \dots (a^{\frac{1}{^{2}}} - a^{\frac{1}{^{2 n + 1}}})} = 0,$ $if a > 1 .$

Smart Achievers · Accepted Answer

(6)

$Statement-I: Use addition theorem of probability$

$Statement-II: Total number of relation both symmetric and reflexive = 2^{(\frac{n^{2} - n}{2})}$

$And total number of symmetric relation = 2^{(\frac{n^{2} + n}{2})}$

$Then number of symmetric relation which are not reflexive = 2^{\frac{n (n + 1)}{2}} - 2^{\frac{n (n - 1)}{2}}$

$= 2^{10} - 2^{6} = 1024 - 64 = 960$

Solution

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Solution

Ans. (6) Statement-I: Use addition theorem of probability Statement-II: Total number of relation both symmetric and reflexive =2(n2-n2) And total number of symmetric relation =2(n2+n2) Then number of symmetric relation which are not reflexive=2n(n+1)2-2n(n-1)2 =210-26=1024-64=960

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