Exams › JEE Main › Maths

Let X = {x1, x2, x3} and Y = {x1, x2, x3, x4, x5}. Which of the following relations is reflexive?

1. R1 = {(x1, x1), (x2, x2)}
2. R1 = {(x1, x1), (x2, x2), (x3, x3)}
3. R3 = {(x1, x1), (x2, x2), (x1, x3), (x2, x4)}
4. R3 = {(x1, x1), (x2, x2), (x3, x3), (x4, x4)}

Correct answer: R1 = {(x1, x1), (x2, x2), (x3, x3)}

Solution

X has three elements x1,x2,x3, so a reflexive relation on X must contain (x1,x1),(x2,x2),(x3,x3) and be a subset of X×X. R={(x1,x1),(x2,x2),(x3,x3)} satisfies this. The option with (x4,x4) is not even a relation on X since x4∉X.

Related JEE Main Maths questions

• Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).
• A real-valued function f(x) obeys the relation f(x-y)=f(x)f(y)-f(a-x)f(a+y), where a is a fixed constant, and f(0)=1. Then the value of f(2a-x) is
• The set of all real values of x for which the function f(x)=(3)/(4-x²)+log₁₀(x³-x) is defined is:
• A relation R is defined on the set of integers Z by the condition that (x,y) belongs to R exactly when x² + y² = 9. Which statement below is false?
• If f(x)=√(1+x²), then which of the following statements is true?
• For the function f(x)=√(x-√(1-x²)), what is its domain?

⚔️ Practice JEE Main Maths free + battle 1v1 →