Q. 5 B4.3( 6 Votes )

# 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

Answer :

Given: A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈A, y ∈A}

To find: the ordered pairs which satisfy the conditions x + y < 5

Explanation: Given: A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈A, y ∈A}

We need to 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, so one of the ordered pairs is (1, 1)

1 + 2 = 3<5, so one of the ordered pairs is (1, 2)

1 + 3 = 4<5, so one of the ordered pairs is (1, 3)

1 + 4 = 5

1 + 5 = 6>5

2 + 1 = 3<5, so one of the ordered pairs is (2, 1)

2 + 2 = 4<5, so one of the ordered pairs is (2, 2)

2 + 3 = 5

2 + 4 = 6>5

2 + 5 = 7>5

3 + 1 = 4<5, so one of the ordered pairs is (3, 1)

3 + 2 = 5

3 + 3 = 6>5

3 + 4 = 7>5

3 + 5 = 8>5

4 + 1 = 5

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

So, the set of ordered pairs satisfying x + y< 5 is {(1,1), (1,2), (1,3), (2, 1), (2,2), (3,1)}.

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