Class 12 Relations And Functions · Case Study5 Marksmixed_relations_and_functions
Class 12 Maths · Relations And Functions · Case Study #65
Voting: properties of a relation
Part (1) 1 Marks
Two neighbours \(X,Y\in I\): \(X\) voted and \(Y\) did not. Which statement is true?
Answer: Option (D): \((X,Y)\notin R\)
- Both members must have voted for the pair to belong to \(R\). Since \(Y\) did not vote, \((X,Y)\notin R\).
Part (2) 1 Marks
Mr. \(X\) and his wife \(W\) both voted. Which statement is true?
Answer: Option (A): Both \((X,W)\in R\) and \((W,X)\in R\)
- Both people voted, so both ordered pairs belong to \(R\).
Part (3) 1 Marks
Three friends \(F_1,F_2,F_3\) all voted. Which statement is true?
Answer: Option (A): \((F_1,F_2)\in R,\ (F_2,F_3)\in R\text{ and }(F_1,F_3)\in R\)
- All three voted, so all pairs displayed in option a are in \(R\).
Part (4) 1 Marks
The above-defined relation R is
Answer: Option (A): Symmetric and transitive but not reflexive
- \(R=V\times V\) is symmetric and transitive. Since \(V\subsetneq I\), some eligible non-voter \(Y\in I\setminus V\) has \((Y,Y)\notin R\). It is therefore not reflexive on \(I\), so option a is correct.
Part (5) 1 Marks
Mr. Shyam voted in the 2019 general election. To whom is he related?
Answer: Option (A): All those eligible voters who cast their votes
- He is related precisely to other members of the actual-voter set, including himself.