A= {(x, y): x, y∈ I, X≥0, y≥0 and 5x + 6y ≤40} B= {(x, y): x, y∈ l, x≥0, y≥0 and 6x + 5y ≤ 40} Where I denotes set of integers, then n(A∩B) is

CBSE Class 11-science Answered

A= {(x, y): x, y∈ I, X≥0, y≥0 and 5x + 6y ≤40} B= {(x, y): x, y∈ l, x≥0, y≥0 and 6x + 5y ≤ 40} Where I denotes set of integers, then n(A∩B) is

Asked by mohvijayjain12 | 22 Jun, 2022, 11:07: AM

Expert Answer

A= {(x, y): x, y∈ I, X≥0, y≥0 and 5x + 6y ≤40} \

B= {(x, y): x, y∈ l, x≥0, y≥0 and 6x + 5y ≤ 40}

The graph is

Therefore, x and y can be equal to or less than 6

When x = 0, there are 7 points

When x = 1, there are 6 points

When x = 2, there are 6 points

When x = 3, there are 5 points

When x = 4, there are 4 points

When x = 5, there are 3 points

When x = 6, there is only one point

Thus, n(A∩B) = 7 + 6 + 6 + 5 + 4 + 3 + 1 = 32

Answered by Renu Varma | 25 Jun, 2022, 11:47: AM

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