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प्रश्न
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y > 8
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उत्तर
A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}
x + y > 8
So, we find the ordered pair such that x + y > 8
Where x and y belongs to set A = {1, 2, 3, 4, 5}
1 + 1 = 2 < 8
1 + 2 = 3 < 8
1 + 3 = 4 < 8
1 + 4 = 5 < 8
1 + 5 = 6 < 8
2 + 1 = 3 < 8
2 + 2 = 4 < 8
2 + 3 = 5 < 8
2 + 4 = 6 < 8
2 + 5 = 7 < 8
3 + 1 = 4 < 8
3 + 2 = 5 < 8
3 + 3 = 6 < 8
3 + 4 = 7 < 8
3 + 5 = 8
4 + 1 = < 8
4 + 2 = 6 < 8
4 + 3 = 7 < 8
4 + 4 = 8
4 + 5 = 9 > 8
So one of the ordered pairs is (4, 5)
5 + 1 = 6 < 8
5 + 2 = 7 < 8
5 + 3 = 8
5 + 4 = 9>8
So one of the ordered pairs is (5, 4)
5 + 5 = 10 > 8
So one of the ordered pairs is (5, 5)
Therefore, the set of ordered pairs satisfying x + y > 8 = {(4, 5), (5, 4), (5, 5)}.
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