Consider the relation R on the set defined by 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 [2026]

Question

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 [2026]

Smart Achievers · Accepted Answer

(1)

R on set ${- 2, - 1, 0, 1, 2}$ , if 1 + ab > 0

R = {(–2, –2), (–1, –1), (0, 0), (1, 1), (2, 2), (–2, –1), (1, 2), (–2, 0), (–1, 0), (1, 0), (2, 0), (–1, –2), (2, 1), (0, –2), (0, –1), (0, 1), (0, 2)}

Number of elements = 17

Clearly, 'R' is reflexive and symmetric but not transitive,

Hence, not an equivalence relation.

$∴$ Only statement I is true.

Solution

Q.
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 [2026]

1 Only I is true

2 Only II is true

3 Both I and II are true

4 Neither I nor II is true

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