Exams › JEE Main › Maths

For the set T = {7, 8, 9}, which of the following relations is reflexive but not transitive?

1. R = {(7,7), (8,8), (9,9), (8,9), (9,7)}
2. R = {(7,8), (8,7), (8,9)}
3. R = {0}
4. R = {(7,8), (8,8), (8,9)}

Correct answer: R = {(7,7), (8,8), (9,9), (8,9), (9,7)}

Solution

Only the first relation contains all three reflexive pairs; it fails transitivity because (8,9) and (9,7) are present but (8,7) is not.

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 →