Ace Test Series: Set Theory & Algebra - Relations

Question

Comments

didnt get u

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the answer is 686. Please explain me!!

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@Rahul. CLosed as duplicate. Check the link.

Answer 1

There are total ⁷C₂ = 21 pairs eligible for symmetric relations.

These pairs are of form {(a,b) (b,a)}. This pair consists of 2 ordered pair (a,b) and (b,a).

Also ordered pair of form (a,a) is also eligible for symmetric relations. There are total 7 such pairs.

Now,

Total number of symmetric relations which contains exactly 4 ordered pair =

⁷C₄ +    //4 ordered pairs of form (a,a)

²¹C₂ +  //2 pairs of form {(a,b) (b,a)} which will give 4 ordered pairs

²¹C₁ * ⁷C₂  //1 pair of form {(a,b) (b,a)} and 2 ordered pairs of form (a,a)

= 686.