What is a Relation – Find Number of Relations – Power Set | CBSE | IIT JEE | BITSAT - Videos

May 15, 2017

190

In this video, we will discuss how a relation is defined in mathematics using Cartesian product of two sets.
Relation defined from set A to B is any subset of A×B.
How we can find the numbers of relations from set A to B containing only “n” number of elements
How to calculate the total number of relations from set A to B if set A contains “m” numbers of elements and set B contains “n” numbers of elements
What is a POWER SET – The set containing all the possible subsets of a set.
How to evaluate the number of elements in a POWER SET.
How the number of elements in a POWER SET is related to number of relations.

We will also discuss, What does it mean by “A binary relation on a set”.
How to find the number of binary relation on set A×B.

Question discussed
JEE Main 2014
A relation on the set A={x : |x| less than 3, x∈Z}, where Z is the set of integers defined by R={(x,y) :y=|x|, x≠1}. Then the number of elements in power set of R is:
(A) 32 (B) 16 (C) 8 (D) 6
ANSWER (B)
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TRY YOURSELF QUESTION
JEE Main 2013 & JEE Main 2015
Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is
(A) 256 (B) 220 (C) 219 (D) 211
ANSWER (C)
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Some Other Important Links are given below:

Mathematical Reasoning IIT JEE Lectures Playlist Link