JEE Mains · Maths · STD 12 - 1. relation and function
Consider the relation R on the set \(\{-2,-1,0,1,2\}\) defined by \((a, b) \in R\) if and only if \(1+ab > 0\). Then, among the statements:
I. The number of elements in R is 17
II. R is an equivalence relation
- A Only I is true
- B Only II is true
- C Both I and II are true
- D Neither I nor II is true
Answer & Solution
Correct Answer
(A) Only I is true
Step-by-step Solution
Detailed explanation
The set is \(A = \{-2, -1, 0, 1, 2\}\). For Statement I, the relation is defined as \((a, b) \in R \iff 1 + ab > 0\). The pairs \((a, b)\) that do not belong to \(R\) satisfy \(1 + ab \le 0 \Rightarrow ab \le -1\). The pairs satisfying \(ab \le -1\) are…
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