The probability that a relation R from <math> <mrow> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>}</mo> </mrow> <mtext> </mtext> <mtext> </mtext> <mi>t</mi> <mi>o</mi> <mtext> </mtext> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>}</mo> </mrow> </mrow> </math> is both symmetric and transitive, is equal to

Total number of possible relation = 2 n 2 = 2 4 = 1 6 Favourable relations = ? , { ( x , x ) } , { ( y , y ) } <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> { ( x , x ) , ( y , y ) } { ( x , x ) , ( y , y ) , ( x , y ) , ( y , x ) } Probability = 5 1 6

The probability that a relation R from <math> <mrow> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>}</mo> </mrow> <mtext> </mtext> <mtext> </mtext> <mi>t</mi> <mi>o</mi> <mtext> </mtext> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>}</mo> </mrow> </mrow> </math> is both symmetric and transitive, is equal to

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Relations and Functions Ncert Solutions Maths class 11th Maths Class 11th

The probability that a relation R from ${x, y} t o {x, y}$ is both symmetric and transitive, is equal to

Option 1 -

$\frac{5}{16}$

Option 2 -

$\frac{9}{16}$

Option 3 -

$\frac{11}{16}$

Option 4 -

$\frac{13}{16}$

2 Views | Posted 2 weeks ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 weeks ago

Correct Option - 1

Detailed Solution:

Total number of possible relation = $2^{n^{2}} = 2^{4} = 16$

Favourable relations = $?, {(x, x)}, {(y, y)}$

${(x, x), (y, y)}$

${(x, x), (y, y), (x, y), (y, x)}$

Probability = $\frac{5}{16}$

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