Reflexive : (a1,b)R(a1,b1)⇒b1=b1 True Symmetric : (a1,b1)R(a2,b2)⇒b1=b2(a2,b2)R(a1,b1)⇒b2=b1} True Transitive : (a1,b1)R(a2,b2)⇒b1=b2&(a2,b2)R(a3,b3)b2=b3⇒(a1,b1)R(a3.b3)⇒ True }b1=b3 Hence Relation R is an equivence relation Statement-I is true. For statement −II⇒y=b so False
Let X= R × R. Define a relation R on X as : (a_1, b_1 ) R (a_2, b_2 ) Leftrightarrow b_1=b_2 Statement I : R is an equivalence relation. Statement II…
JEE Main 2025 — Mathematics Algebra
2025mcqeasy
Let X=R×R. Define a relation R on X as : (a1,b1)R(a2,b2)⇔b1=b2 Statement I : R is an equivalence relation. Statement II : For some (a,b)∈X, the set S={(x,y)∈X:(x,y)R(a,b)} represents a line parallel to y=x. In the light of the above statements, choose the correct answer from the options given below :
Official previous-year question
Held on 23 Jan 2025 · Verified 6 Jul 2026.
Options
- A
Both Statement I and Statement II are false
- B
Statement I is true but Statement II is false
- C
Both Statement I and Statement II are true
- D
Statement I is false but Statement II is true
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