Join now for JEE/NEET and also prepare for Boards Join now for JEE/NEET and also prepare for Boards. Register Now
Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
Q: let S={1,2,3,4} The total number of unordered pairs of disjoint subsets of S is equal to (A)26 (B)34 (C)42 (D)41 pls explain what the phrase"unordered pairs of disjoint subsets mean"? Q: let S={1,2,3,4} The total number of unordered pairs of disjoint subsets of S is equal to (A)26 (B)34 (C)42 (D)41pls explain what the phrase"unordered pairs of disjoint subsets mean"?
We first count the number of ordered pairs of disjoint subsets of S. For each element of S, we can choose to put it in either set A, set B, or neither (but not both), so we are making a sequence of 4 elements with 3 options each time. There are thus 3^4 different sequences ofchoices, and each results in a distinct ordered pair of subsets.As it is unordered pair- so we dont have to worry about the order. Hence,If A and B are distinct, there are exactly two ordered pairs, (A,B) and (B,A), foreach unordered pair, otherwise there is just one. Given that A and B are disjointthe only case where they are identical is when they are both empty. Thus thereare (3^4-1)/2 + 1 unordered pairs of disjoint subsets of S.The answer = 41ThanksBharat BajajIIT Delhiaskiitians faculty
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
points won -