Question

Let S = {1, 2, 3, …., 20}

R₁ = {(a, b) : a divide b}

R₂ = {(a, b) : a is integral multiple of b} a, b ∈ s

n(R₁ – R₂) = ?

Answer 1

R₁ = {(1, 1), (1, 2), (1, 3)…., (1, 20), (2, 2), (2, 4)….(2, 20), (3, 3), (3, 6), ….(3, 18), (4, 4), (4, 8), … (4, 20), (5, 5), (5, 10), (5, 15), (5, 20), (6, 6), (6, 12), (6, 18), (7, 7), (7, 14), (8, 8), (8, 16), (9, 9), (9, 18), (10, 10), (10, 20), (11, 11), (12, 12), ….(20, 20)}

n(R₁) = 66

R₂ = {a is integral multiple of b}

So n(R₁ – R₂) = 66 – 20 = 46

as R₁ \(\cap\) R₂ = {(a, a) : a \(\in\) s} = {(1, 1), (2, 2)…, (20, 20)}