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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 = 5
उत्तर
A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}
x + y = 5
So, we find the ordered pair such that x + y = 5
Where x and y belongs to set A = {1, 2, 3, 4, 5}
1 + 1 = 2 ≠ 5
1 + 2 = 3 ≠ 5
1 + 3 = 4 ≠ 5
1 + 4 = 5
⇒ the ordered pair is (1, 4)
1 + 5 = 6 ≠ 5
2 + 1 = 3 ≠ 5
2 + 2 = 4 ≠ 5
2 + 3 = 5
⇒ the ordered pair is (2, 3)
2 + 4 = 6 ≠ 5
2 + 5 = 7 ≠ 5
3 + 1 = 4 ≠ 5
3 + 2 = 5
⇒ the ordered pair is (3, 2)
3 + 3 = 6 ≠ 5
3 + 4 = 7 ≠ 5
3 + 5 = 8 ≠ 5
4 + 1 = 5
⇒ the ordered pair is (4, 1)
4 + 2 = 6 ≠ 5
4 + 3 = 7 ≠ 5
4 + 4 = 8 ≠ 5
4 + 5 = 9 ≠ 5
5 + 1 = 6 ≠ 5
5 + 2 = 7 ≠ 5
5 + 3 = 8 ≠ 5
5 + 4 = 9 ≠ 5
5 + 5 = 10 ≠ 5
Therefore, the set of ordered pairs satisfying x + y = 5 = {(1, 4), (2, 3), (3, 2), (4, 1)}.
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