If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true? Class 9

If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true? Class 9

Question 1.

If x ≠ y, then (x, y) ≠ (y, x); and (x, y) = (y, x) if and only if x = y. Is this claim true? Class 9

Answer:

Yes, the claim is true.

If x ≠ y

For example, let x = 2 and y = 3, then

(x, y) = (2, 3) and (y, x) = (3, 2)

∴ (x, y) ≠ (y, x)

If x = y

For example, let x = y = 4, then

(x, y) = (4, 4) and (y, x) = (4, 4)

∴ (x, y) = (y, x)

Question 2.

On a graph sheet, mark the x-axis and y-axis and the origin O. Mark points from (-7, 0) to (13, 0) on the x-axis and from (0, -15) to (0,12) on the y-axis. (Use the scale 1 cm = 1 unit.) Class 9

Solution: