Question

If R = {(x, y): x, y ∈ Z, x² + 3y² ≤ 8} is a relation on the set of integers Z, then the domain of R^–1 is ______.

विकल्प

• {–1, 0, 1}

• {–2, –1, 1, 2}

• {0, 1}

• {–2, –1, 0, 1, 2}

Answer 1

If R = {(x, y): x, y ∈ Z, x² + 3y² ≤ 8} is a relation on the set of integers Z, then the domain of R^–1 is {–1, 0, 1}.

Explanation:

If R = {(x, y): x, y ∈ Z, x² + 3y² ≤ 8}

x = 1, –1, y = –1, 0, 1

x = 2, –2, y = 1, –1, 0

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

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

Domain of R^–1 = {–1, 0, 1}