Let R = {(x, y) : x, y Z, y = 2x − 4}. If (a, −2) and (4, b2)R, then write the values of a and b.

Here,R={(x,y) : x, yϵZ, y=2x-4}Now,(a,-2)ϵ R ⇒ -2=2a-4∴ 2a=-2+4∴ 2a=2∴ a=1Also,(4,b2)ϵ R ⇒ b2=2×4-4∴ b2=8-4∴ b2=4∴ b=±2

Q7 of 76 Page 2

Let R = {(x, y) : x, y Z, y = 2x − 4}. If (a, −2) and (4, b²)R, then write the values of a and b.

Here,R={(x,y) : x, yϵZ, y=2x-4}

Now,(a,-2)ϵ R ⇒ -2=2a-4

∴ 2a=-2+4

∴ 2a=2

∴ a=1

Also,(4,b²)ϵ R ⇒ b²=2×4-4

∴ b²=8-4

∴ b²=4

∴ b=±2

If R is a relation from set A = {11, 12, 13} to set B = {8, 10, 12} defined by y = x − 3, the write R⁻¹.

Let A = {1, 2, 3} and R = {(a, b) : | a²− b² | ≤5, a, b A}. Then write R as set of ordered pairs.

If R = {(2, 1), (4, 7), (1, −2), ...}, then write the linear relation between the components of the ordered pairs of the relation R.

If A = {1, 3, 5} and B = {2, 4}, list the elements of R, if R = {(x, y) : x, yA × B and x > y}.